School committee is very awesome

Probability Level 1

A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is $\text{\_\_\_\_\_\_\_\_\_\_}$ .

2100 8 10 15

2 solutions

Pham Khanh
Apr 26, 2016

There are $C_{2}^5$ ways to select 2 teachers from 5 teachers.There are also $C_{4}^{10}$ ways to choose 4 students out of 10 students. Because we need to do both things, use product rule : $C_{2}^5 \times C_{4}^{10}=\frac{5!}{2! \times 3!} \times \frac{10!}{4! \times 6!}=$ $=\frac{4 \times 5}{1 \times 2} \times \frac{7 \times 8 \times 9 \times 10}{1 \times 2 \times 3 \times 4}$ $=10 \times 210$ $=\LARGE \boxed{2100}$

The Combination is $C_2^5$ and $C_4^{10}.$ .

You have reversed the combination.

Or simply denote the combination as $C \dbinom{5}{2}$

Samara Simha Reddy - 5 years, 1 month ago

Thanks. Edited. By the way, nice profile picture

Pham Khanh - 5 years, 1 month ago

Thank You.

Samara Simha Reddy - 5 years, 1 month ago

Luvneesh Kumar
Apr 25, 2016

P (5,2)=》 the ways to select 2 teachers P (10,4)=》to select 4 students

Sunce we have to do both use product rule

Ps . Just see the options in this one :)

School committee is very awesome

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