Tricky Permutations & Combinations Question

[nanor]

You know combinations suck when even the teacher needs to read off the sheet :P

[cryonim]

Here's how I learnt it from the video and processed it.

When there are lesser positions than the elements to pick or choose from we can’t simply divide by the overcounting. This is because it is not certain that for each arrangement there is the repeated element.
For ex.:
ALGEBRA and pick/choose 3.
But when we do 7C3/2! and 7P3/2!, we get a fractional number and that does not make sense as there can either be a possibility or none, not in between.
So to solve it we divide it into sub-arrangements and then add all them up.

For Combination,
First, no As: 5 total letters and 3 positions so 5C3 = 10
Then, 1 A: This A takes a guaranteed slot so only 2 positions left, 5C2 = 10
Then, 2 A: Similarly to 1 A, 5C1 = 5


And total is 25, which is our answer. As we see different types of combinations, ones without A, ones with a single A and ones with one more A as that’s the total no. of As, and adding them up are the total combinations for 3 positions.
Alternatively, we could directly just take 1 A and say ALGEBR, and in that case we just simply do 6C3, and this includes combinations with 1 A and no A. Which can be seen as it equals 20. Now we only need to see combinations with both As and when 2 A take up the slots, we are left with 1 position and 5 letters giving us 5 and total being 25.


Similarly, for Permutations,
First no As, 5P3 = 60
Then 1 A, 5P2 = 20
However, since order matters here, the 1 A’s place matters as well, as we know
A _ _
_ A _
_ _ A
are the 3 positions, we multiply 5P2 with 3
Then 2 A, 5P1 = 5
Similarly, these 2 A’s non identical positons matter as well and that gives us 15.

Total is 135.

Alternatively, we can directly take ALGEBR and that gives us 6P3 which is the sum of permutations achieved through 1 A and no As with order in mind, and it is indeed equal to 120 which we got from 5P3 + 5P2*3. And we follow the same last step which gives us 15 and the total is 135.

[shakilahammed]

it's still quite hard to understand

[souljacem]

You're saving my life. I love you

[dabien]

I will forever remember "you must think *thunk*" 4:58

[footballmagic]

My brain: confusion of the highest orda!!

[ravenousturtle]

I came with a more difficult variant of this type of question.
How many ways are there of a) selecting and b) arranging, four letters of the word "connection"?



The answers which I arrived at were 98 ways of selecting along with 1960 for arranging.

[amritacharya]

Beautifully explained sir! Great job :)

[rose-umjt]

THANK this helped me figure out some problems !

[elementalneil]

Oh man, your videos make me speechless

[geoffphillips]

Why do you say 6x5x4 is 6P4? Sorry I'm confused; isn't it 6P3?

[bashirbandi]

@4:43
6P4 = 360
awesome explanation btw ! :)

[abrocks]

A video on permutation of
numbers being divisible by 125 formed using 0, 2, 5, 1, 8 repetition allowed?

[alvarolealjr]

im getting murdered by a problem. 4 greeting cards, mary selects 3. what are the total selections? now the answer is 20 but i have no clue why

[mellee]

i dont get it!!!! why did you choose 3 out of 5 samples in combination in your first example @2:50

[yizizheng]

At 4:38 why are there 3 ways of doing them?