being good at maths is not enough for Oxbridge interviews

Added: 2026-05-09

[00:00:00]Today I'm going to be going through how to explain a concept in an Oxford or Cambridge maths interview. So if you're someone who's looking to apply to Oxford or Cambridge, of course you've got to do the interviews to get an offer. And today I'm going to be explaining or showing you how to explain a concept in maths so you can replicate this in your interview. By the way, if you've never seen me before, my name's Jam. I study maths at the University of Oxford. And now I've helped over a 100 different students secure Oxford and Cambridge maths offers. And by the way, just check out the scenery here. It's absolutely beautiful. really really gorgeous.

[00:00:30]Anyway, I've got a little whiteboard with me and we'll be looking at this word here, statistics. We're not actually going to be doing any statistics, but we're going to be using this word uh as a nice little question.

[00:00:40]So, the question is this. How many rearrangements of the letters in this word are there? So, there's 1 2 3 4 5 6 7 8 9 10 different letters in the word statistics. And we want to know how many ways are there to rearrange these 10 letters and create different strings of 10 letter words. Now this is a very like common type of interview question and crucially is important that we explain our answer. Loads of people whenever I make these sorts of videos will just comment, oh the answer is this and they'll just write down a number and it's like well great but that's not what's going to get you that Oxbridge offer. It's really knowing how to explain your ideas clearly. Let's have a look. So I'm going to imagine as if I was in an Oxbridge interview. I've just been asked this question. Let's get stuck in. Okay, awesome. So the idea here is to think about the number of uh sort of rearrangements of these 10 letters. So in order to answer that, what we want to do is firstly kind of tackle what would happen if all these letters were different and answer the question then. But obviously here we've got some repeated letters like three S's, three T's, two I's. And so we've just got to be careful about those uh and not double counting or triple counting etc. Okay. So let's imagine we did have 10 different letters here. So, we'll call this S1, this one S2, and this one S3, just to for the time being make make it look like they're different. And same with the T's, T1, T2, and T3. And then same with the I.

[00:01:59]So, we've got I1 and I2, like so. And of course, there's only one A and one C, so we can just leave those as they are.

[00:02:05]Now, if there were 10 different genuinely different letters, and we're looking at the number of rearrangements of those 10 letters, well, there would be 10 factorial different ways of arranging those. So if you just think 1 2 3 4 5 6 7 8 9 10. Imagine we wanted to make a 10 letter word, but we have 10 choices for which letter can go in the first place. Let's say we choose I2. Uh we could put maybe T3 in the next one and so on. So we got 10 choices for this guy, but once we've chosen I2, we can't choose that again. So we're left with nine. So we get nine choices for that and so on. Then eight, then seven, and so on all the way down to one. We multiply these together and we get 10 factorial different ways of arranging the words uh the letters in the word statistics if we assume they are all 10 different letters. However, of course, there aren't actually 10 different letters in the word statistics. So, let's look at the the eyes to begin with. So, the idea here is in any of these 10 factorial words, we could just swap the two eyes. So for example, if we take the word statistics, which is one of our 10 factorial different words, I could also create the word S1. Oh, I write it down here. S1, T1, A, T2, and then I2, S2, uh, T3, I1, C, S3. And so it's the exact same word except I swap I1 and I2. And the idea is I could do that with any of these 10 factorial words. Just swap the I1's and the I2s. And so for every single genuine word, so the actual word statistics without these like ones and twos and threes and the subscripts, the actual word statistics appears twice in this list because of or at least twice because of the fact that I can swap the two eyes. And so I need to divide by two um to accommodate for this because there's two different arrangements of uh where I can swap the eyes. But in the same way I could be thinking about the T's for example. So with any word statistic, if I just focus on the T's here, I could have T1, T2, T3 kind of appearing in that order or in any kind of rearrangement of these three letters.

[00:04:09]So I could have T3, T2, and then T1 or T2, T3, T1, and so on. And so I need to ask myself, how many rearrangements are there of these three letters? And these are distinct. So it's just going to be three factorial. There will be three factorial rearrangements of those three distinct objects. And so in a similar way, every single three three factorial is six. Each of these words, just if we look at rearranging the T's, we have six of them. So we also need to divide by six. And using a similar logic, we do the same for the S's. And we also divide by six. So I've put 2 * 6 * 6. But normally it's nicer if we just use factorials. 2 factorial, 3 factorial, 3 factorial, like so. And that is the number of rearrangements of the letters in the word statistics. And that's how you would explain something in an Oxford/Cambridge interview. You're not assuming any prior knowledge, at least nothing that's too beyond um the basics, the stuff that maybe you'd see in A level. So this is not something that you'd be asked to explain in an A level.

[00:05:06]Uh like well actually maybe you could uh but something that you wouldn't be asked to explain in a GCSE. So anything be before GCSE you can kind of assume is fine. Um but here you wouldn't be asked in GCSE to explain the number of rearrangements of these words. So you've got to make it nice and clear. It's not enough to just say this um you know just say this number right um what you could do is if you wanted to if you could just say this answer at the start of your interview and say okay this is the answer there's 10 factorial divided by two factorial 3 factorial uh 3 factorial if you want I can try and explain this in a bit more depth blah blah blah but likelihood is they already want you to explain this in a lot of depth anyway um but cool in an Oxford interview though do be warned that the questions will be a lot harder than this the purpose of this video is mostly just to show you how to actually explain in concepts nice and clearly in an Oxbridge interview.

[00:05:52]I'll leave another video on screen where I solve an Oxbridge interview problem.