College Algebra

Question

A TV studio has brought in 9 boy kittens and 7 girl kittens for a cat food commercial. 

The director is going to choose 7 of these kittens at random to be in the commercial.

What is the probability that the director chooses 4 boy kittens and 3 girl kittens? Round your answer to three decimal places.

Answer 1

(9 choose 4)(7 choose 3) /all divided by/ (16 choose 7)

9*8*7*6 7*6*5

--------- * ------------

4*3*2 3*2

===================================

16*15*14*13*12*11*10

----------------------

7*6*5*4*3*2

top left: 8*6 is 48 and 4*3*2=24, so they cancel

top right: 6 cancels 2*3

denominator: 14 cancels 7*2

12 cancels 6

10 cancels 5

16 cancels 4

15 cancels 3

9*7*2 * 7*5

------------------

4*5*13*2*11*2

5 cancels

2 cancels

9*7*7

-------

4*13*2*11

441/ 1144

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