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14 students have volunteered for a committee. Eight of them are seniors and six of them are juniors.

(a) How many ways are there to select a committee of 5 students?

(b) How many ways are there to select a committee with 3 seniors and 2 juniors?

(c) Suppose the committee must have five students (either juniors or seniors) and that one of the five must be selected as chair. How many ways are there to make the selection?

Respuesta :

Answer: a) 2002, b) 840, c) 10010.

Step-by-step explanation:

Since we have given that

Number of students = 14

Number of students senior = 8

Number of students junior = 6

(a) How many ways are there to select a committee of 5 students?

Here, n = 14

r = 5

We will use "Combination" for choosing 5 students from 14 students.

[tex]^{14}C_5=2002[/tex]

(b) How many ways are there to select a committee with 3 seniors and 2 juniors?

Again we will use "combination":

[tex]^8C_3\times ^6C_2\\\\=56\times 15\\\\=840[/tex]

(c) Suppose the committee must have five students (either juniors or seniors) and that one of the five must be selected as chair. How many ways are there to make the selection?

So, number of ways would be

[tex]^{14}C_5\times ^5C_1\\\\=2002\times 5\\\\=10010[/tex]

Hence, a) 2002, b) 840, c) 10010.

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