Number of ways of selecting r consecutive things out of n things

The number of ways of selecting ' n ' things out of '3n ' things of which 'n ' are of one kind and alike and 'n ' are of second kind and alike and the rest unlike is :

Number of ways of selecting one or more things out of n dissimilar things are

Number of ways of selecting one or more things out of n dissimilar things are

Number of ways of selecting one or more things out of n dissimilar things are

If N denotes the number of ways of selecting r objects of out of n distinct objects (rgeqn) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .^(r-1)C_(r-n) b. .^(r-1)C_n c. .^(r-1)C_(n-1) d. none of these

Which of the following is not the number of ways of selecting n objects from 2n objects of which n objects are identical

If the number of ways of selecting r balls with replcement out of n balls numbered 1,2,3……,100 such that the largest number selected is 10 is 271, then r= (A) 4 (B) 5 (C) 3 (D) none of these

If the number of ways of selecting 3 numbers out of 1, 2, 3, ……., 2n+1 such that they are in arithmetic progression is 441, then the sum of the divisors of n is equal to

If the number of ways of selecting n cards out of unlimited number of cards bearing the number 0,9,3, so that they cannot be used to write the number 903 is 96, then n is equal to

Find the number of ways of selecting 10 balls out of an unlimited number of identical white, red, and blue balls.