Mathematics 2004 JAMB Past Questions - Question 47: A committee of six is to be formed by a state governor from nine state House of Assembly .In how many ways can the members of the committee be chosen so as to include one member of the house of Assembly ?

Correct Answer

D

Explanation

To form a committee of six members that includes one member of the House of Assembly, we can consider two cases:Case 1: Selecting one member from the House of Assembly and five members from the remaining eight members.Case 2: Selecting all six members from the remaining eight members.For Case 1:The number of ways to select one member from the House of Assembly is 9C1 = 9.The number of ways to select five members from the remaining eight members is 8C5 = 56.Therefore, the number of ways to form the committee in Case 1 is 9 * 56 = 504.For Case 2:The number of ways to select all six members from the remaining eight members is 8C6 = 28.Therefore, the number of ways to form the committee in Case 2 is 28.To find the total number of ways to form the committee, we add the results from Case 1 and Case 2:3 x 9 x 2 x 7 = 378Therefore, there are 378 ways to form the committee of six members that includes one member of the House of Assembly.