How many ways can you select a committee of 3 from a group of 5 people?

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How many ways can a committee of three be chosen from a group of ten people? How many ways are there to choose a president, secretary, and treasurer.

I know that on the first part I have to use the combination formula since order doesn't matter. Then $\frac{n!}{r!(n-r)!} \rightarrow \frac{10!}{3!(10-3)!}$= 120.

The second part requires order meaning that I need to use the permutation formula $\frac{n!}{(n-r)!}$ $\rightarrow$ $\frac{10!}{(10-3)!}$ = 720.

Is my process correct?

This is a combination problem, since the order of selection is not significant. Standard notation for this can be written C(5,3), and most standard calculators can be used to do the calculation without even understanding it. However, understanding it, you can calculate the product of three numbers beginning at 5 and counting down: 5 times 4 times 3, and then divide by the product of the three numbers beginning at 3 and counting down: 3 times 2 times 1.

Final answer is (5*4*3) over (3*2*1) or 60/6 = 10.

Since n=5 and r=3 (five people taken three at a time), then the equation is as follows Use the following formula for combinations nCx=(n,x)=n!/x!(n-x) Looks confusion doesn't it. n=5 x=3 Now solve 5 x 4 x 3 x 2 x 1 _________________ 3 x 2 x 1 x 2 x 1 You can cross out or multiply and divide. 120/12 = 10