A camera shop stocks eight different types of batteries, one of which is type A7

Question

A camera shop stocks eight different types of batteries, one of which is type A76. 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?

c) How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?

Explanation / Answer

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

Nos of ways = nCr = 30C8

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?

taking four A76 batteries as a single unit, the out of 26 batteries, they can distribute among theirselves,

Nos of ways = 26C8 * 4C4 = 26C8

c) How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?

for at most three mean, three or less than 3.

Nos of way = 30C7 + 29C7 * 1C1 + 28C7 * 2C2 + 27C7 * 3C3 = 30C7 + 29C7 + 28C7 + 27C7

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