(a) The number of ways to select a committee of five from a class of 30 students is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of students, k is the number of students to select, and "!" denotes factorial.

So, C(30, 5) = 30! / [5!(30-5)!] = 142506 ways.

(b) After the committee is selected, one person is elected chairperson and another is elected secretary. The number of ways to fill these positions is given by the permutation formula P(n, k) = n! / (n-k)!, where n is the total number of committee members and k is the number of positions to fill.

So, P(5, 2) = 5! / (5-2)! = 20 ways.

Therefore, the committee can be selected in 142506 ways and the positions of chairperson and secretary can be filled in 20 ways.

Question

(a) The number of ways to select a committee of five from a class of 30 students is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of students, k is the number of students to select, and "!" denotes factorial.

So, C(30, 5) = 30! / [5!(30-5)!] = 142506 ways.

(b) After the committee is selected, one person is elected chairperson and another is elected secretary. The number of ways to fill these positions is given by the permutation formula P(n, k) = n! / (n-k)!, where n is the total number of committee members and k is the number of positions to fill.

So, P(5, 2) = 5! / (5-2)! = 20 ways.

Therefore, the committee can be selected in 142506 ways and the positions of chairperson and secretary can be filled in 20 ways.

Knowee AI · Accepted Answer

(a) The number of ways to select a committee of five from a class of 30 students is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of students, k is the number of students to select, and "!" denotes factorial.

So, C(30, 5) = 30! / [5!(30-5)!] = 142506 ways.

(b) After the committee is selected, one person is elected chairperson and another is elected secretary. The number of ways to fill these positions is given by the permutation formula P(n, k) = n! / (n-k)!, where n is the total number of committee members and k is the number of positions to fill.

So, P(5, 2) = 5! / (5-2)! = 20 ways.

Therefore, the committee can be selected in 142506 ways and the positions of chairperson and secretary can be filled in 20 ways.

A committee of five is to be selected from a class of 30 students.(a) In how many ways can this be done?(b) After the committee is selected, one person is elected chairperson and another is elected secretary. In howmany ways can these positions be filled?

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