SOLUTION: An English reading list has 10 American novels and 7 English novels. A student must read 4 from the list, and at least 2 must be American novels. In how many different ways can the

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Question 1149049: An English reading list has 10 American novels and 7 English novels. A student must read 4 from the list, and at least 2 must be American novels. In how many different ways can the 4 books be selected?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


4, 3, or 2 of the 4 must be American novels.

(1) 4 American: choose 4 of the 10 American AND 0 of the 7 English.
C%2810%2C4%29%2AC%287%2C0%29

OR

(2) 3 American, 1 English: choose 3 of the 10 American AND 1 of the 7 English.
C%2810%2C3%29%2AC%287%2C1%29

OR

(3) 2 American, 2 English: choose 2 of the 10 American AND 2 of the 7 English.
C%2810%2C2%29%2AC%287%2C2%29

ANSWER:

C%2810%2C4%29%2AC%287%2C0%29%2BC%2810%2C3%29%2AC%287%2C1%29%2BC%2810%2C2%29%2AC%287%2C2%29

Use a calculator if necessary.

If you want practice calculating these kinds of numbers, perform the similar calculations to find the numbers of ways of choosing either 1 or 0 American novels; then verify that the sum of all the numbers you have calculated is equal to C(17,4), the total number of ways of selecting 4 of the 17 novels.