Question

3.A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?
144
72
36
665,280

4.In how many different orders can you line up 8 cards on a table?

8
1
1,680
40,320

5.There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?

1 way
90 ways
3,628,800 ways
45 ways

Answer 1

The correct answers are: #3) 72; #4) 40,320; #5) 90.

Explanation:
#3) The number of possible choices are found by multiplying the choices of flavors and the choices of toppings:
6*12=72.

#4) The ordering of 8 cards is a permutation, given by 8!=40,320.

#5) This is a permutation of 10 objects taken 2 at a time:
P(10,2) = 10!/(10-2)!=10!/8!=90.