If ¹²P_r = ¹¹P₆ + 6 ¹¹P₅, then r =

The number of numbers greater than 1000 but not greater than 4000 that can be formed with the digits 0,1,2,3,4 repetition of digits being allowed is

If ²⁰P_r : ²⁰P_r-1 = 15 : 1 then r =

Two dice are rolled simultaneously. The probability of getting an even number and an odd number is

In an experiment of rolling 2 dice, the probability that, the dots on the second die is less than that on the first die is

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one each in a box could be placed such that a ball does not go to a box of its own colour is

The number of 5 digit numbers of different digits can be formed with 2 even and 3 odd digits is

The number of ways a pack of 52 cards can be divided amongst four players in 4 sets, three of them having 17 cards each and the fourth one just 1 card is

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