A camera shop stocks eight different types of batteries, one of which is type a7b. assume there are at least 30 batteries of each type.

a. how many ways can a total inventory of 30 batteries be distributed among the eight different types?

b. how many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four a76 batteries?

Question

Mathematics

Boston Shepherd

1 February, 09:21

A camera shop stocks eight different types of batteries, one of which is type a7b. assume there are at least 30 batteries of each type.

a. how many ways can a total inventory of 30 batteries be distributed among the eight different types?

b. how many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four a76 batteries?

+1

Answers (1)

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Bud · Answer 1

Statistical Method

For A:

Given:

k = 30

n = 8

Solution:

where! = factorial

the required number is:

C (30 + 8 - 1, 30) = C (37, 30)

=37! / (37 - 30) ! (30) !

= 10295472

For B:

Given:

k = 26

n = 8

Solution:

the require number is:

C (26 + 8 - 1, 26) = C (33,26)

= 33! / (33 - 26) ! (26) !

= 4272048

The answers are 10295472 for (a) and 4272048 for (b)