A collage committee is formed with $5$ student and $2$ professors when $8$ student and $5$ professors and available. How many such committees can be formed ?

Open in App

Solution

$5$ student out of $8$ can be selected in $_{5}^{8} C$ ways.
$2$ professors out of $5$ can be selected in $_{2}^{5} C$ ways.
Therefore, by the fundamental principle of counting, 5 student out of 8 and 2 professors out of 5 can be selected in
$_{5}^{8} C \times_{2}^{5} C = \frac{8!}{3! 5!} \times \frac{5!}{2! 3!} = 560$ ways

Suggest Corrections

Similar questions

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is be formed. Find the number of ways in which this can be done. Further find in how many of these committees :

(i) A particular professor is included.

(ii) A particular student is included.

(iii) A particular student is excluded

Q. There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
(i) a particular professor is included.
(ii) a particular student is included.
(iii) a particular student is excluded.

Q. There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further, find in how many of these committees
(i)A particular professor is included
(ii)A particular student is included (iii) A particular student is excluded.

In a college there are 20 professors including the principal and the vice principal. A committee of 5 is to be formed. In how many ways it can be formed so that neither the principal nor the vice principal is included?

Q. There are

10

professors and

20

lecturers, out of whom a committee of

2

professors and

3

lecturers is to be formed. Which of the following options is (are) CORRECT?

Join BYJU'S Learning Program

A collage committee is formed with 5 student and 2 professors when 8 student and 5 professors and available. How many such committees can be formed ?

5 student out of 8 can be selected in 85C ways.2 professors out of 5 can be selected in 52C ways.Therefore, by the fundamental principle of counting, 5 student out of 8 and 2 professors out of 5 can be selected in85C×52C=8!3!5!×5!2!3!=560 ways

A collage committee is formed with $5$ student and $2$ professors when $8$ student and $5$ professors and available. How many such committees can be formed ?