Statement 1: Number of ways in which India can win the series of 11 matches is`2^(10)` . (if no match is drawn). Statement 2: For each match there are two possibilities, India either wins or loses.

Find the number of ways in which India can win the series of 11 matches (If no match is drawn and all matches are played).

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

Statement 1: Number of ways in which 30 can be partitioned into three unequal parts, each part being a natural number is 61. Statement 2; Number of ways of distributing 30 identical objects in three different boxes is ^30 C_2dot

Statement 1: the number of ways of writing 1400 as a product of two positive integers is 12. Statement 2: 1400 is divisible by exactly three prime factors.

Statement 1: Number of ways in which Indian team (11 players) can bat, if Yuvraj wants to bat before Dhoni and Pathan wants to bat after Dhoni is 11!/3!. Statement 2: Yuvraj, Dhoni, and Pathan can be arranged in batting order in 3! ways.

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

Statement 1: the number of ways in which n persons can be seated at a round table, so that all shall not have the same neighbours in any two arrangements is (n-1)!//2. Statement 2: number of ways of arranging n different beads in circles is (n-1)!//2.

Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ^9C_3 . Statement-2 : The number of ways of choosing any 3 places from 9 different places is ^9C_3 . Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true.

The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find the mean, median and mode of these scores

The probability of India winning a test match againest England is (2)/(3) . Assuming independence from match to match, the probability that in a 7 match series India's third win occurs at the fifth match, is