Statement 1: Number of ways of selecting 10 objects from 42 objects of which 21 objects are identical and remaining objects are distinct is `2^(20)dot` Statement 2: `^42 C_0+^(42)C_1+^(42)C_2++^(42)C_(21)=2^(41)dot`

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is

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

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)

Statement 1: When number of ways of arranging 21 objects of which r objects are identical of one type and remaining are identical of second type is maximum, then maximum value of ^13 C_ri s78. Statement 2: ^2n+1C_r is maximum when r=ndot

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

The number of ways of arranging n(gt2) distinct objects in a line so that two particulars objects are never together is

""^21C_0 + ""^21C_1 + ""^21C_2 + ……..+ ""^21C_10 =

Find the sum of the series ^10 C_0+^(10)C_1+^(10)C_2++^(10)C_7dot

Number of ways in which two persons A and B select objects from two different groups each having 20 different objects such that B selects always more objects than A (including the case when A selects no object) is (2^(40)-^(40)C_(21))//2.

Statement-1: The total number of ways in which three distinct numbers in AP, can be selected from the set {1,2,3, . .,21}, is equal to 100. Statement-2: If a,b,c are inn AP, then a+c=2b.