determining the number of possible groups of elements\nten students need to present their reports. five can…

determining the number of possible groups of elements\nten students need to present their reports. five can present each day. how many ways can the teacher choose a group of five students to present their reports on the first day?\nhow many ways can the teacher choose a group of 5 students to present on the first day if marjorie must present on the first day?

determining the number of possible groups of elements\nten students need to present their reports. five can present each day. how many ways can the teacher choose a group of five students to present their reports on the first day?\nhow many ways can the teacher choose a group of 5 students to present on the first day if marjorie must present on the first day?

Answer

Answer:

  1. 252
  2. 126

Explanation:

Step1: Recall combination formula

The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen.

Step2: Calculate first - part

For choosing 5 students out of 10 to present on the first day, $n = 10$ and $r=5$. So $C(10,5)=\frac{10!}{5!(10 - 5)!}=\frac{10!}{5!×5!}=\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}=252$.

Step3: Calculate second - part

If Marjorie must present, we need to choose 4 more students out of the remaining 9 students. Here $n = 9$ and $r = 4$. So $C(9,4)=\frac{9!}{4!(9 - 4)!}=\frac{9!}{4!×5!}=\frac{9\times8\times7\times6}{4\times3\times2\times1}=126$.