Assume that you have 5 different types of vegetables and 10 different types of fruit. a vegetable salad consists of a mixture of any 3 types of vegetables, and a fruit salad consists of a mixture of 2 kinds of fruit. (1) in how many different ways can you prepare a vegetable salad and a fruit salad?

10 different vegetable salads 45 different fruit salads. The formula for picking m of n items is n!/(m! (n-m)!). To show how this formula works, let's deal with the vegetable salad problem. This problem involves using factorials. N factorial is simply 1 times 2 times 3 times ... N. This represents the number of ways you can arrange N objects and is written as N!. So imagine for the vegetable salad, you place on the table all 5 different vegetables and select the 1st 3 of the arrangement. For 5 vegetables, you can arrange them in 5! ways which is 1 * 2 * 3 * 4 * 5 = 120 different arrangements. You pick the 1st 3 vegetables and you're left with 2 vegetables you haven't selected. There are 2! ways for those leftover vegetables to ordered which is 2! = 1 * 2 = 2 and you really don't care what their order is, so divide the 120 by 2 giving you 60 different ways that you could have picked up the 3 vegetables you are going to use. But does it really matter about the order you picked up those 3 vegetables? No it doesn't. So divide once again by 3! giving you 60 / 6 = 10 different possible vegetable salads. If we had plugged in the numbers we get 5!/(3!(5-3)!) = 120/(6(2)!) = 120/(6*2) = 120/12 = 10. Now for the fruit salad, we can plug in the numbers getting 10!/(2!(10-2)!) = 3628800 / (2(8)!) = 3628800/(2*40320) = 3628800/80640 = 45 different fruit salads

Hello!

the answer is:

the answer is:

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!