The number of ways in which 5 red balls and 4 black balls of different sizes can be arranged in a row so that two balls of the same colour come together is

The number of 3 letter words formed that containing atleast one vowel from the letters a,b,c,d,e,f is

The number of four digited numbers which are not divisible by 5 that can be formed from by using the digits 0,2,4,5 is

In a class of 10 students, there are 3 girls A,B,C.The number of different ways that they can be arranged in a row such that no two of the three girls are consecutive is

A boats crew consists of 16 men, 6 of whom can only row on one side and 4 only on the other. The number of ways in which the crew can be arranged 8 on each side is

In how many ways 4 sovereigns be given away, when there are 5 applicants and any applicant may have either 0,1,2,3or4 sovereigns?

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