Find the number of selections of one or more things from the group of p identical things of one type, q identical things of another type, r identical things of the third type and n different things.

Explanation

Since number of ways of selecting r things out of n identical things =1 for al `r le n`.
Number of ways of selecting zero or more things out of p identical things = p+1
Similarly, number of ways of selecting zero or more things out of q and r identical things is q+1 and r+1 respectively.
Also, number of ways of selecting zero or more things out of n different things `=2xx2xx2xx..` n times `=2^(n)`
Therefore, total number of ways of selecting zero or more things out of all given things
`=(p+1)(q+1)(r+1)2^(n)`
But number of ways of selecting one or more things out of given things `=(p+1)(q+1)(r+1)2^(n)-1`.