Question

From a group of 10 people, 5 are selected at random to participate in a game show. In how many ways can the 5 people be selected? A. 120 B. 252 C. 30,240 D. 100,000

Answer 1

A) 120

Explanation:

For this question you will need to use factorials

5! =5×4×3×2×1

which equals to 120

therefore the 5 people can be selected in 120 different ways

hope this helps

Answer 2

The correct option is B. 252

Explanation:

Total number of peoples in the group = 10

Number of peoples needed to be selected from the group of 10 peoples = 5

We need to find the total number of ways in which we can select the 5 peoples.

`\text{So, Number of ways of selecting the 5 people out of 10 = }_5^7 \txterm{C}`

`\text{So, Number of ways of selecting the 5 people out of 10 = }(10!)/(5!* 5!)`

`\text{So, Number of ways of selecting the 5 people out of 10 = }252`

Hence, Total number of required ways = 252

Therefore, The correct option is B. 252