The total number of ways of selecting two numbers from the set `{1,2, 3, 4, ........3n}` so that their sum is divisible by 3 is equal to a. `(2n^2-n)/2` b. `(3n^2-n)/2` c. `2n^2-n` d. `3n^2-n`

the total number of ways of selecting two number from the set {1,2,3,4,…..3n} so that their sum divisible by 3 is equal to -

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

The probability that a randomly selected 2-digit number belongs to the set { n in N: (2^(n)-2) is a multiple of 3} is equal to

If 1+(1+2)/2+(1+2+3)/3+ddotto\ n terms is Sdot Then, S is equal to a. (n(n+3))/4 b. (n(n+2))/4 c. (n(n+1)(n+2))/6 d. n^2

Prove by induction that the sum S_(n)=n^(3)+2n^(2)+5n+3 is divisible by 3 for all n in N.

n is selected from the set {1,2,3,............,100} and the number 2^(n)+3^(n)+5^(n) is formed.Total number of ways of selecting n so that the formed number is divisible by 4 is equal to (A)50(B)49(C)48 (D) None of these.

If n is a natural number, then which of the following is not always divisible by 2? 1.) n^2-n 2.) n^3-n 3.) n^2-1 4.) n^3-n^2

Prove that the number of ways to select n objects from 3n objects of whilch n are identical and the rest are different is 2^(2n-1)+((2n)!)/(2(n!)^(2))

Let N denotes the number of ways in which 3n letters can be selected from 2n A's, 2nB's and 2nC's. then,