Rewrite the statement using mathematical symbols 28) pis the set of even numbers less than 50 and more than 40, use the fundamental counting principle to solve the problem. 29) a restaurant offers 7 entrees and 11 desserts. in how many ways can a person or two-course meal? 30) in how many ways can a girl choose a two-piece outfit from 5 blouses and 7 skirts? 31) how many ways are there to arrange 6 unique cd's in order along a shelf?

28) The required statement is P = {2x: x ∈ N, 20<N<25}.28)

29) There are 77 ways in which a person can select two-course meal.

30) There are 35 ways in which she can choose a two piece outfit.

31) There are 720 ways to arrange 6 unique CD's in order along a shelf.

Step-by-step explanation:

Consider the provided information.

28) P is the set of even numbers less than 50 and more than 40,

Rewrite the statement using mathematical symbols.

Let x ∈ N then 2x ∈ N where 2x is a even number.

We want the value of real number should be more than 40 and less than 50.

That means the value of 2x is more than 40 and less than 50.

Or the value of x is more than 20 and less than 25.

Thus, the required statement is P = {2x: x ∈ N, 20<N<25}.

29) A restaurant offers 7 entrees and 11 desserts. In how many ways can a person or two-course meal?

Here, two independent events are involved: selecting a entrees and selecting a dessert.

The first event can occur in 7 ways and the second in 11 ways.

Thus,   7 · 11 = 77

Hence, there are 77 ways in which a person can select two-course meal.

30) In how many ways can a girl choose a two-piece outfit from 5 blouses and 7 skirts?

Here, it is given that girl want a two piece outfit.

For blouses she has 5 choices and for skirts she has 7 choices.

The first event can occur in 5 ways and the second in 7 ways.

Thus,   5 · 7 = 35

Hence, there are 35 ways in which she can choose a two piece outfit.

31) How many ways are there to arrange 6 unique CD's in order along a shelf?

Let us consider you have 6 unique CD's and you want to put them on shelf.

So you will start with the first CD. You have 6 choices, and you select one of them.

For second CD you have now 5 choices, because one CD is already on the shelf.

For Third CD you have now 4 choices, because two CD are already on the shelf. Similarly for all.

This can be written as: 6×5×4×3×2×1 = 6! = 720 ways

Hence, there are 720 ways to arrange 6 unique CD's in order along a shelf.

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