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At the grocery store, Howard has narrowed down his selections to 3 vegetables, 4 fruits, 6 cheeses, and 8 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 8 whole grain breads?

Respuesta :

Answer:

1,716

Step-by-step explanation:

Given that

Number of vegetables = 3

Number of Fruits = 4

Number of Cheeses = 6

Number of whole grain breads = 8

Number of bought items = 15

Number of whole grain breads = 8

The calculation of number of ways if all 8 whole grain breads is shown below:-

Number of ways if all 8 whole grain breads =  [tex]^7C_7 \times ^1^3C_7[/tex]

=  [tex]1\times\dfrac{13\times12\times11\times10\times9\times8\times7\times6!}{6!\times7\times6\times5\times4\times3\times2\times1}[/tex]

= 1,716