BTGmoderatorLU wrote:A class consists of 5 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
A. 9
B. 18
C. 32
D. 60
E. 240
The OA is C.
Please, can somebody explain when to make the sum of combinations and when to do the product of combinations? Thanks!
The class consists of 5 boys and 4 girls.
Given: One kid can only hold one title
Number of ways a boy can be selected as the class clown = 5;
Number of ways a boy can be selected as the teacher's pet = 4; Since one boy is already selected a clown, the number of boys left = 4
This is a case of AND, so we multiply the number of ways
Number of ways 2 boys of the class can be the class clown AND the teacher's pet = 5*4 = 20 ---(1)
Number of ways a girl can be selected as the most beautiful girl = 4;
Number of ways a girl can be selected as the smartest kid = 3; Since one girl is already selected as the most beautiful girl, the number of girls left = 3
This is a case of AND, so we multiply the number of ways
Number of ways 2 girls of the class can be the most beautiful girl AND the smartest kid = 4*3 = 12 ---(2)
Since the situation is that we have to choose either 2 boys OR 2 girls, we will add the total number of ways [(1) + (2)].
Total number of ways = 20 + 12 = 32
The correct answer:
C
Hope this helps!
-Jay
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