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Keep all ten seats when people are absent

A group of 10 people consists of 3 married couples and 4 single men.

(a) A committee of 4 is to be formed from the 10 people.

(i) How many different committees can be formed?

(ii) How many different committees can be formed if the committee can consist of at most 1 married couple?

(iii) How many different committees can be formed if the committee consists of at least one man and at least one woman?

(b) The group sits at a round table with 10 seats.

(i) If each man sits next to his wife, how many ways can they be seated?

(ii) If one particular man is absent and the rest are allowed to sit without any restrictions, how many ways can they be seated?

(iii) If a particular couple is absent and the rest are allowed to sit without any restrictions, how many ways can they be seated?

[2009/CJC/II/8(modified)]

CJC · Discussion · Question 12

Empty seats remain part of the circular arrangement.

Read the worked solution