A TV studio has brought in 8 boy kittens and 9 girl kittens for a cat food commercial. The director is going to choose 11 of these kittens at random to be in the commercial. What is the probability that the director chooses 4 boy kittens and 7 girl kittens? Round your answer to three decimal places.

0.204

Step-by-step explanation:

The formula to use to solve this is the combination formula.

Combination formula =

C(n, r) = nCr = n!/r! (n - r)!

Total number of kittens = 8 boy kittens + 9 girl kittens

= 17 kittens

Step 1

We find the probability of choosing 4 boy kittens out of 8 boy kittens

= 8C4 = 8!/4! × (8 - 4)!

= 8C4 = 8! / 4! × 4!

= 8C4 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1)

8C4 = 70

Step 2

We find the probability of choosing 7 girl kittens out of 9 girl kittens

9C7 = 9!/7! × (9 - 7)!

= 9C7 = 9! / 7! × 2!

= 9C7 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (7 × 6 × 5 × 4 × 3 × 2 × 1) × (2 × 1)

9C7 = 36

Step 3

Find the probability of Picking 11 kittens out of 17 kittens

17C11 = 17!/11! × (17 - 11)!

= 17C11 = 17! / 11! × 6!

= 17C11 = 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)

17C11 = 12,376

Step 4

The final step

The probability that the director chooses 4 boy kittens and 7 girl kittens

= 8C4 × 9C7/ 17C11

= 70 × 36/12376

= 2520/12376

= 0.2036199095

Approximately to 3 decimal places = 0.204

Therefore, the probability that the director chooses 4 boy kittens and 7 girl kittens is 0.204

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40