Home
Class 12
MATHS
Let S={1,2,3ddot,9}dotFork=1,2, 5,l e t...

Let `S={1,2,3ddot,9}dotFork=1,2, 5,l e tN_k` be the number of subsets of S, each containing five elements out of which exactly `k` are odd. Then `N_1+N_2+N_3+N_4+N_5=?` 210 (b) 252 (c) 125 (d) 126

A

210

B

252

C

126

D

125

Text Solution

Verified by Experts

The correct Answer is:
C
`N_(i) = ""^(5)C_(k) xx ""^(4)C_(5 - k)`
`N_(1) = 5 xx 1`
`N_(2) = 10 xx 4`
`N_(3) = 10 xx 6`
`N_(4) = 5 xx 4`
`N_(5) = 1`
`N_(1) + N_(2) + N_(3) + N_(4) + N_(5) = 126`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the number of subsets of A if A = { X : X = 4n +1, 2 lt= n lt= 5, n in NN }

Let E={1,2,3,4}a n dF={1,2}dot If N is the number of onto functions from EtoF , then the value of N//2 is

Let A be a set of n(geq3) distance elements. The number of triplets (x ,y ,z) of the A elements in which at least two coordinates is equal to a. ^n P_3 b. n^3-^n P_3 c. 3n^2-2n d. 3n^2-(n-1)

A is a set containing n different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P . A subset Q of A is again chosen. The number of ways of choosing P and Q so that PnnQ contains exactly two elements is (a). .^n C_3xx2^n (b). .^n C_2xx3^(n-2) (c). 3^(n-1) (d). none of these

If n >1 , the value of the positive integer m for which n^m+1 divides a=1+n+n^2+ddot+n^(63) is/are 8 b. 16 c. 32 d. 64

Suppose A is a complex number and n in N , such that A^n=(A+1)^n=1, then the least value of n is a. 3 b. 6 c. 9 d. 12

Prove that 4n^(2)-1 is an odd number for all n in N

The number of possible outcomes in a throw of n ordinary dice in which at least one of the die shows and odd number is a. 6^n-1 b. 3^n-1 c. 6^n-3^n d. none of these

Let n_1ltn_2ltn_3ltn_4ltn_5 be positive integers such that n_1+n_2+n_3+n_4+n_5="20. then the number of distinct arrangements n_1, n_2, n_3, n_4, n_5 is

Let f(n)=sum_(k=1)^(n) k^2(n C_k)^ 2 then the value of f(5) equals