ten students need to present their reports. five can present each day. how many ways can the teacher choose…

ten 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? how 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?

ten 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? how 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

Explanation:

Step1: Calculate combinations for first - part

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 10$ (total students) and $r=5$ (students to be chosen). $C(10,5)=\frac{10!}{5!(10 - 5)!}=\frac{10!}{5!×5!}=\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}=252$

Step2: Calculate combinations for second - part

Since Marjorie must present on the first day, we need to choose 4 more students out of the remaining 9 students. Using the combination formula with $n = 9$ and $r = 4$. $C(9,4)=\frac{9!}{4!(9 - 4)!}=\frac{9!}{4!×5!}=\frac{9\times8\times7\times6}{4\times3\times2\times1}=126$

Answer:

252 126