A bouquet of 5 roses is made from 8 pink roses and 7 white roses:

1. Find the number of bouquets of 5 roses.
2. Find the number of bouquets of 5 roses in which three are pink and two are white.
3. Find the number of bouquets of 5 roses composed of all pink or all white roses.
4. Find the number of bouquets of 5 roses with three or more white roses

This question just does not make any sense to me. The wording seems off...

I understand that the wording of the question may seem confusing or unclear. Let's break it down step-by-step to better understand it and find the answers.

1. To find the number of bouquets of 5 roses, we need to consider the total number of roses available (8 pink roses + 7 white roses). In this case, there are 15 roses in total.
To select a bouquet of 5 roses, we can use the concept of combinations. The formula for the number of combinations can be written as C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items we want to select.
Substituting the values, we get C(15, 5) = 15! / (5!(15-5)!).
Solving this expression, we find that there are 3,003 bouquets of 5 roses.

2. To find the number of bouquets of 5 roses with three pink and two white roses, we can use the same concept of combinations.
We need to select 3 pink roses from the available 8 pink roses, and 2 white roses from the available 7 white roses.
Using the combinations formula, we get C(8, 3) * C(7, 2) = (8! / (3!(8-3)!)) * (7! / (2!(7-2)!)). Simplifying this expression, we find that there are 560 bouquets with three pink and two white roses.

3. To find the number of bouquets of 5 roses composed of all pink or all white roses, we need to consider two separate cases:
a) Bouquet with all pink roses: We have 8 pink roses available, so there is C(8, 5) = 8 possible bouquets.
b) Bouquet with all white roses: We have 7 white roses available, so there is C(7, 5) = 21 possible bouquets.
Therefore, there are a total of 8 + 21 = 29 bouquets composed of all pink or all white roses.

4. To find the number of bouquets of 5 roses with three or more white roses, we can consider three scenarios:
a) Bouquets with exactly 3 white roses: We need to select 3 white roses from the available 7 white roses, and 2 remaining roses from the remaining 8 pink roses. So the number of bouquets is C(7, 3) * C(8, 2).
b) Bouquets with exactly 4 white roses: We need to select 4 white roses from the available 7 white roses, and 1 remaining rose from the remaining 8 pink roses. So the number of bouquets is C(7, 4) * C(8, 1).
c) Bouquets with exactly 5 white roses: We need to select all 5 white roses from the available 7 white roses. So the number of bouquets is C(7, 5).

Adding the results from each scenario, we find that there are a total of C(7, 3) * C(8, 2) + C(7, 4) * C(8, 1) + C(7, 5) bouquets of 5 roses with three or more white roses.

I hope this explanation helps clarify the question and how to find the answers.