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.

Answer 2

By finding the numbers of combinations, we will see:

• a) 72 choices.
• b) 40,320 options.
• c) 45 ways.

How many different choices are there?

There are 6 different flavors, and 12 different toppings. So, if we can select only one flavor and one topping, the total number of different choices that there are is:

C = 6*12 = 72

So there are 72 choices.

b) In how many different orders can you line up 8 cards on a table?

Because order matter, here the number of combinations is 8 factorial, or:

8! = 8*7*6*...*3*2 = 40,320

c) The first two positions out of 10 can be selected in N ways, such that:

$N = C(10, 2) = \frac{10!}{(10 - 2)!*2!} = \frac{10*9}{2} = 45$

So there are 45 ways.

If you want to learn more about combinations:

https://brainly.com/question/11732255

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