Statement 1: number of ways in which 10 identical toys can be distributed among three students if each receives at least two toys is `.^6C_2`. Statement 2: Number of positive integral solutions of `x+y+z+w=7i s^6C_3dot`

Find the number of ways in which 8 non-identical apples can be distributed among 3 boys such that every boy should get at least 1 apple and at most 4 apples.

The number of positive integral solutions of x^4-y^4=3789108 is a. 0 b. 1 c. 2 d. 4

Number of ways in which Rs. 18 can be distributed amongst four persons such that nobody receives less than Rs. 3 is a. 4^2 b. 2^4 c. 4! d. none of these

The number of ways of distributing 3 identical physics books and 3 identical mathematics books among three students such that each student gets at least one books is

Statement 1: The number of positive integral solutions of a b c=30 is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is 3^3 (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: let E={1,2,3,4}a n dF={a ,b} Then the number of onto functions from EtoF is 14. Statement 2: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Number of ways in which 30 identical things are distributed among six persons is a .^17C_5 if each gets odd number of things b .^16C_11 if each gets odd number of things c .^14C_5 if each gets even number of things (excluding 0) d .^15C_10 if each gets even number of things (excluding 0)

Find the number of positive integral solutions satisfying the equation (x_1+x_2+x_3)(y_1+y_2)=77.

Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement -I : Number of terms in the expansion of (x+y+z+w)^(50) is .^(53)C_(3) . Statement -II : Number of non- negative solution of the equation p+q+r+s=50 is .^(53)C_(3) .