Question

Hosea's doctor has recommended that his daily diet should include 4 vegetables, 3 fruits, and 3 whole grains. At the grocery store, Hosea has a choice of 16 vegetables, 11 fruits, and 7 whole grains. In how many ways can he get his daily requirements if he doesn't like to eat 2 servings of the same thing in 1 day

Answer 1

10510500

Explanation:

Given :

Recommended daily diet :

Vegetables = 4 ; Fruits = 3 ; Whole grains = 3

Available choices :

Vegetables = 16 ; Fruits = 11 ; While grains = 7

Using the combination relation ; The number of ways in which daily requirement can be gotten is

Vegetable = 16C4

Fruits = 11C3

Whole-grains = 7C3

Recall:

nCr = n! ÷ (n-r)!r!

Using calculator :

16C4 * 11C3 * 7C3

1820 * 165 * 35

= 10510500