Problem 7

Probability Level 2

I have to pick 4 pamphlets and 7 brochures from a stack of 7 pamphlets and 12 brochures. In how many ways can I make the choices if the order doesn't matter?

Check out the set: Combinatorics .


The answer is 27720.

Angela Fajardo by Angela Fajardo , 19, Philippines

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2 solutions

Ashish Menon
Sep 6, 2016

Selecting 4 pamplets out of 7 = 7 C 4 ^7C_4 .
Selecting 7 pamplets out of 12 = 12 C 7 ^{12}C_7 .

So, the number of ways = 7 C 4 × 12 C 7 = 35 × 792 = 27720 ^7C_4 × ^{12}C_7\\ = 35 × 792\\ = \color{#3D99F6}{\boxed{27720}} .

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Zee Ell
Aug 29, 2016

The number of ways to choose 4 pamphlets out of 7:

( 7 4 ) = 35 { 7 \choose 4} = 35

The number of ways to choose 7 brochures out of 12:

( 12 7 ) = 792 { 12 \choose 7} = 792

By combining these choices, we get:

35 × 792 = 27720 35 × 792 = \boxed {27720}

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