Discrete math problem on Combinations. These problems involve a fruit store !!

Posted on 2014-12-03 06:58:00 in Math by KEN

a. How many ways are there to select a bag 10 fruits?
(The order of selecting the fruits is not important.)

I used nCk for this one. where n=10 and k =4 and ended up with 210 ways. Is this correct?

b. How many ways are there to select a bag of 10 fruits if there are only 4 pears available?
(The grocery store only has 4 pears left.)

I'm assuming I use my previous answer and subtract the possible number where there are more than 4 pears.

c. How many ways are there to select a bag of 10 fruits if there are only 4 pears and 4
oranges available?
(The grocery store only has 4 pears and 4 oranges left.)

d. You can also buy a closed paper bag containing 10 fruit, but you can’t peek inside till
you purchase it.

What is the smallest number of the most frequent fruit in any possible bag of 10 fruit?

(For example, if the bag contains 2 apples, 5 pears and 3 oranges, then the most frequent
fruit is the pear, or if the bag contains 4 pears, 4 apples and 2 bananas, then the pears
and apples are the most frequent fruit and so 4 is the number of the most frequent fruit.)

This part I'm just confused or I'm just really tired.

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