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18 May 2021, 02:30
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E
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Difficulty:
45%
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Question Stats:
63% (01:19) correct
37%
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wrong
based on 177
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A class consists of 6 boys and 5 girls. In how many ways can the teacher pick two different boys to be class clown and teacher's pet and two different girls to be best dressed and smartest kid on the block?
A. 6×5×5×4/2
B. 6×5×5×4/4
C. 6×6×5×5/2
D. 6×6×5×5/4
E. 6×5×5×4
A. 6×5×5×4/2
B. 6×5×5×4/4
C. 6×6×5×5/2
D. 6×6×5×5/4
E. 6×5×5×4
18 May 2021, 02:39
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6P2 * 5P2 = 6X5X5X4
Since all 4 awards are unique, we will us permutation instead of combination.
Choice for 1st award : 6 boys
Choice left for 2nd award : 5 Boys
So 2 awards among 6 boys can be given in 6*5 ways
Similarly, 2 unique awards among 5 girls be given in 5*4 ways
Multiply both of them, as they are mutually exclusive events.
Since all 4 awards are unique, we will us permutation instead of combination.
Choice for 1st award : 6 boys
Choice left for 2nd award : 5 Boys
So 2 awards among 6 boys can be given in 6*5 ways
Similarly, 2 unique awards among 5 girls be given in 5*4 ways
Multiply both of them, as they are mutually exclusive events.
18 May 2021, 02:46
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As there are 6 boys, we are picking 1 of the 6 to be class clown, and then 1 of 5 to be teacher's pet as one was already selected to be the class clown. In other words, there are 6 possible choices for class clown and 5 possible choices for teacher's pet. So for the boys we have 6*5
We do the same with the girls. 1 of the 5 girls will be best dressed, and 1 of the 4 remaining girls will be the smartest girl on the block. For the girls we have 5*6
Together that gives us: 6*5*5*4
Answer E
We do the same with the girls. 1 of the 5 girls will be best dressed, and 1 of the 4 remaining girls will be the smartest girl on the block. For the girls we have 5*6
Together that gives us: 6*5*5*4
Answer E
