brandon is helping his younger brother wrap presents for the holidays. they have 61 different rolls of…

brandon is helping his younger brother wrap presents for the holidays. they have 61 different rolls of wrapping paper, including 54 rolls with an owl design and 6 with a holiday - themed design.\nif brandons brother randomly chooses 58 rolls of wrapping paper to wrap the first group of presents, what is the probability that 53 of the chosen rolls of wrapping paper have an owl design and 5 have a holiday - themed design?\nwrite your answer as a decimal rounded to four decimal places.

brandon is helping his younger brother wrap presents for the holidays. they have 61 different rolls of wrapping paper, including 54 rolls with an owl design and 6 with a holiday - themed design.\nif brandons brother randomly chooses 58 rolls of wrapping paper to wrap the first group of presents, what is the probability that 53 of the chosen rolls of wrapping paper have an owl design and 5 have a holiday - themed design?\nwrite your answer as a decimal rounded to four decimal places.

Answer

Explanation:

Step1: Calculate total combinations

We use the combination formula (C(n,r)=\frac{n!}{r!(n - r)!}), where (n) is the total number of items and (r) is the number of items to be chosen. The total number of ways to choose 58 rolls out of 61 is (C(61,58)=C(61,3)=\frac{61!}{3!(61 - 3)!}=\frac{61\times60\times59}{3\times2\times1}=35990).

Step2: Calculate favorable combinations

The number of ways to choose 53 owl - designed rolls out of 54 is (C(54,53)=\frac{54!}{53!(54 - 53)!}=54). The number of ways to choose 5 holiday - themed rolls out of 6 is (C(6,5)=\frac{6!}{5!(6 - 5)!}=6). The number of favorable combinations is the product of these two combinations, so (C(54,53)\times C(6,5)=54\times6 = 324).

Step3: Calculate the probability

The probability (P) is the number of favorable combinations divided by the total number of combinations. So (P=\frac{324}{35990}\approx0.0090).

Answer:

0.0090