A class consists of 15 students. The instructor wants to pick a group of 4 to wo

Question

A class consists of 15 students. The instructor wants to pick a group of 4 to work on a special project. How many different groups of 4 can he choose? a) 1365 b) 720 c) 450 d) 55 If a class consists of 15 students: 10 girls and 5 boys, how many different groups of 4 are made up of 2 boys and 2 girls? a) 1365 b) 720 c) 450 d) 55 In a marketing survey consumers are asked to give their first three choices, in order of preference, of 9 different drinks. In how many different ways can they indicate their choices? a) 504 b) 14 c) 45 d) 729 How many different license plates can be made using 3 digits followed by 3 letters if the first digit must be greater than or equal to 5 and no repetition of letters is allowed? a) 8, 788, 000 b) 12, 654, 720 c) 15, 600, 000 d) 7, 800, 000

Explanation / Answer

1) Total no. of students =15

The number of groups that can be formed with 4 students out of 15 =15C4=1365

So correct answer is (a)

2) no, of boys =10. Then 2 boys out of these 10 can be selected in 10C2=45ways

no. of girls =5. Then 2 girls out of these 5 can be selected in 5C2=10ways

Total no. of ways to select a group of 4 (2boys and 2 girls) students =45*10=450

The correct answer is (c)

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