A teacher\'s kindergarten class consists of 10 girls and 8 boys. (a) The teacher

Question

A teacher's kindergarten class consists of 10 girls and 8 boys. (a) The teacher wants to select 1 girl and 1 boy to be class representatives. Is how many ways can this be done? (b) The teacher wants to send 2 of the boys to the library to get some boles. In how many ways can the teacher select the two boys? In order to help organize a bake sale, the teacher wants to appoint a committee of 3 students to help out. One of the three students chosen will be designated as Chairperson. In how many ways can this committee be chosen if the chairperson must be a girl? (d) The teacher wants to divide the class into team for a hockey game team is to consist of 5 girls and 4 boys. In how many ways can this be

Explanation / Answer

10 girls and 8 boys are there in total.

a. 1 girl , 1 boy as representatives can be choosen in:10C1 *8C1 = 10*8 = 80 ways

b. Choosing 2 boys from 8 boys can be done in 8C2 = 8*7/2 = 28 ways

c. 1 girl is chairperson. That can happen in 10C1 ways. So we are left with 9 girls and 8 boys. So, 2 remaining members can be choosen from 9+8 =17 students in 17C2 ways. So, 10C1*17C2 = 10*17*16/2 = 1360 ways

d. This can be done in : Choosing any 5 girls and 4 boys from the groups , the remiaing will be 2nd team. So, 10C5*8C4 = 17640 ways to do this.

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