The probability that in a family of 4 children there will be at least one boy is

The number of ways that all the letters of the word SWORD can be arranged such that no letter is in its original position is

A set contains (2n+1) elements. The number of subsets of the set which contain more than n elements is

The number of arrangements of arranging 6 players to throw the cricket ball so that the oldest player may not throw first is

The number of 6 digited numbers which are not divisible by 5 that can be formed with the digits 4,5,6,7,8,9 is

The number of numbers less than 2000 that can be formed using the digits 1,2,3,4 when repetition is allowed is

A: If there are 8 points in a plane no three of which are on the same straight line except 4 points are collinear then the number of straight lines formed by joining them is 23

R: If there are n points in a plane no three of which are on the same straight lie except p points are collinear then the number of straight lines formed by joining them is ⁿC₂ – ^pC₂ +1

If a denotes the number of permutations of x+2 things taken all at a time, b the number of permutations of x-11 things taken all at a time such that a=182bc, then the value of x is

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is

The number of ways in which 7 distinct boys can be distributed among 3 children when each child is eligible to take all the toys is