Can you list down every selection ?

Probability Level 4

$\large \boxed{A,A,A,A,A,B,B,B,B,C,C,C,D,D \ }$

How many total selections of $5$ letters from the above $14$ letters are possible ?

Try more combinatorics problems.

The answer is 41.

2 solutions

Vaibhav Prasad
Apr 3, 2015

If there are $m$ items of one kind, $n$ items of another kind and so on, then the number of ways of selecting $r$ things is given by

$\text{the coefficient of } x^r \text{in the expansion of :}$

$(1+x+x^2+x^3.....x^m)(1+x+x^2+x^3.....x^n).........$

Applying this here gives us coefficient of $x^5$ as $41$

Do you know its proof? From where did you learn this?

Adarsh Kumar - 6 years, 2 months ago

nope sorry...

just read it somewhere !!

Vaibhav Prasad - 6 years, 2 months ago

ok!thanx! BTW from where did you come to know about that juggler's problem,or did you make it yourself?and did you know about that formula which you used?

Adarsh Kumar - 6 years, 2 months ago

@Adarsh Kumar – The juggler problem was from my fiitjee book. the question had me lost for about half an hour and after that when i solved it i found the problem interesting so i posted it. the formula that i used, i came up with it while solving the problem.

Vaibhav Prasad - 6 years, 2 months ago

@Vaibhav Prasad – ok nice!thanx!

Adarsh Kumar - 6 years, 2 months ago

Why isn't the answer ${ 14 }^{ 5 }$ ?

Aryan Gaikwad - 5 years, 11 months ago

Easy question did it the same way....

Divyansh Choudhary - 5 years, 6 months ago

Prakhar Bindal
Mar 2, 2016

I Made 6 simple cases

Case 1. All 5 Alike = 1 way

Case 2. 4 Alike 1 Different = 2*3 = 6 ways

Case3. 3 Alike 2 Different = 3*3 = 9 ways

Case 4. 2 Alike 3 different = 4*1 = 4 ways

Case 5. 2 Alike 2 Alike 1 Different = 6*2 = 12 ways

Case 6. 3 Alike 2 Alike = 3*3 = 9 ways

Can you list down every selection ?

Try more combinatorics problems.

The answer is 41.

2 solutions

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