In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
Answer(s): C
You must multiply your options to every item. (2 shelves) x (4 beds) x (3 closets + 7 chairs) = 80 possibilities.
In how many combinations can we choose 2 students out of 10 if each student is needed to fill a different roll in the student’s council?
For the first roll there are 10 free students, for the second roll there are only 9 left. Therefore, we have (10 x 9) 90 combinations total.
Three people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?
Answer(s): B
Treat the two who must sit together as one person. You have two possible sitting arrangements. Then remember that the two that sit together can switch places. So you have two times two arrangements and a total of four.
How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and the other digits are all different from each other?
For the first digit you have 9 options (from 1 to 9 without 0), for the second number you have 9 options as well (0 to 9 minus the first digit that was already used) and for the third digit you have 8 options left.So the number of possibilities is 9 x 9 x 8 = 648.
Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
Answer(s): D
There are (8 x 9) 72 possibilities of shirts + pants. (2 x 3) 6 Of the combinations are not allowed. Therefore, only (72 – 6) 66 combinations are possible.
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