Question

How many arrangements can you make with 5 flowers chosen from 7 red and 8 white flowers? If you want to pick six flowers and have two white flowers in the middle two spots, how many combinations are possible?

a) 15,120 arrangements; b) 1,680 combinations
b) 56,700 arrangements; b) 336 combinations
c) 7,560 arrangements; b) 56,700 combinations
d) 336 arrangements; b) 1,680 combinations

Answer 1

There are 3003 possible arrangements for choosing 5 flowers out of a total of 15 (7 red and 8 white). For six flowers with two specific white flowers in the middle, there are 1001 possible combinations.

Step-by-step explanation:

To determine how many arrangements one can make with 5 flowers out of 7 red and 8 white flowers, we simply compute the combination of 15 flowers taken 5 at a time. We use the formula for combinations, which is C(n, k) = n! / [k!(n - k)!], where 'n' is the total number of items and 'k' is the number of items to choose.

For the first situation, this gives us C(15, 5) = 15! / (5!10!) = 3003 arrangements.

For the second part, if we want six flowers with two specific white flowers in the middle, we first place those two white flowers which leaves us with 4 spots to fill and 14 flowers remaining (since we've used 2 of the 8 white flowers). The remaining spots can be filled with any of the remaining flowers, so we have C(14, 4) combinations for the other 4 spots.

The calculation is C(14, 4) = 14! / (4!10!) = 1001 combinations.