A club consists of 15 males and 11 females A in how many way

A club consists of 15 males and 11 females:

A. in how many ways can a subcommittee of 3 males and 2 females be formed?

b. a president and a secretary are to be chosen respectivly how many choices are possible if the secretary must be female

Solution

a) Out of 15 males and 11 females a commitee of 3 males and 2 females can be formed as follows:

¹⁵C_{3 *} ¹¹C₂ = [(15! ) / (3! * 12!) ] * [(11! ) / (2! * 9!) ]

= [(15 * 14 *13 )/ (3*2)] * [(11 * 10 )/ (2)]

= 455 * 55 = 25025 ways

Therefore, a subcommittee of 3 males and 2 females can be formed in 25025 ways

b) A president and a secretary can be chosen so that secretary is a female in following way

= ( President male and secretary female) + ( President and secretary both females)

= ¹⁵C_{1 *} ¹¹C₁ + ¹¹C_{2 =} { [(15! ) / (1! * 14!) ] * [(11! ) / (1! * 10!) ] } + { 11! / (2! * 9!)}

= { 15 *11} + {(11 * 10) / 2}

= 165 * 55 = 9075 ways

Therefore, a president and a secretary can be choosen in 9075 ways so that secretary must be female