Question

An art collection on auction consisted of 4 Dalis, 5 van Goghs, and 6 Picassos. Atthe auction were 5 art collectors. If a reporter noted only the number of Dalis, van Goghs, andPicassos acquired by each collector, how many different results could have been recorded if allof the works were sold?

Answer 1

Answer:

1852200

Explanation:

The number of ways in which all the works are sold = Number of ways of the selling of 4 Dalis × Number of ways of the selling of 5 van Goghs × Number of ways of the selling of 6 Picassos.

Also, number of ways in which n things can be distributed into k things are = $^{n+k-1}C_{k-1}$

k = 5

Thus,

Number of ways = $^{4+5-1}C_{5-1}\times ^{5+5-1}C_{5-1}\times ^{6+5-1}C_{5-1}$ = $^{8}C_{4}\times ^{9}C_{4}\times ^{10}C_{4}$ = 1852200