There are 7 different varieties of fruit, and Al is determined to buy no more than one of any variety?

Question

How many different orders can he place?

Prob and stat math class....I know the answer is 127...just don't see how they get it...

Answer 1

There are 2 choices for each of 7 varieties, so you can express the total number of choices as 2^7.

However, one of those choices would be to buy no fruit at all, so you must eliminate that choice: 2^7 - 1, which equals 127.

Answer 2

This is a problem with combinations. You have to use the formula for picking 'k' thinkgs from a group of 'n' things. The formula for combinations is:

Number of ways to pick k from n is = n!/(k!*(n-k)!)

Now -- lets see what we can do.

There are 7 varieties & you can only pick one of each type (at most).

There is one way you can pick seven varieties.

There are seven ways you can pick six varieties (7!/(6!*1!))

There are 21 ways that you can pick five of the seven varieties

There are 35 ways that you can pick four of the seven varieties

There are 35 ways that you can pick three of the seven varieties

There are 21 ways that you can pick two of the seven varieties

There are seven ways that you can pick one of the seven varieties

127 = 7+21+35+35+21+7+1

Answer 3

Using binary, you use a 7 "bit" equation. Order one is 0000001, or no apple, no banana, no cherry, no lemon, no lime, no melon, yes starfruit. Similarly, you get orders 0000010, 0000011, etc.

Obviously, the answer is 0000001 to 1111111, excluding the 0000000, since that is no order. Converting the binary to decimal you get 1 to 127.

Answer 4

Ask your math teacher