a hockey coach was taking her team out to a picnic lunch to celebrate their first win. she made 9…

a hockey coach was taking her team out to a picnic lunch to celebrate their first win. she made 9 sandwiches, 7 of which were hummus. if ants randomly chose to nibble on 6 of the sandwiches, what is the probability that all of them are hummus? write your answer as a decimal rounded to four decimal places.

a hockey coach was taking her team out to a picnic lunch to celebrate their first win. she made 9 sandwiches, 7 of which were hummus. if ants randomly chose to nibble on 6 of the sandwiches, what is the probability that all of them are hummus? write 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 sandwiches and $r$ is the number of sandwiches ants choose. Here, $n = 9$ and $r=6$. So, $C(9,6)=\frac{9!}{6!(9 - 6)!}=\frac{9!}{6!3!}=\frac{9\times8\times7}{3\times2\times1}=84$.

Step2: Calculate favorable combinations

The number of hummus - sandwiches is $7$, and we want to choose $6$ of them. Using the combination formula with $n = 7$ and $r = 6$, we get $C(7,6)=\frac{7!}{6!(7 - 6)!}=\frac{7!}{6!1!}=7$.

Step3: Calculate probability

The probability $P$ that all 6 chosen sandwiches are hummus is the ratio of the number of favorable combinations to the total number of combinations. So, $P=\frac{C(7,6)}{C(9,6)}=\frac{7}{84}=\frac{1}{12}\approx0.0833$.

Answer:

$0.0833$