(i): If ¹²C_r+1=¹²C_3r-5, then r=3 or 4

(ii): ⁹C₃+⁹C₅=¹⁰C_r, then r=4 or 6

The sum of numbers formed by talking all the digits 2,4,6,8 is

The sum of all four digited that can be formed, using  the digits 0,2,4,7,8 without repetition is

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 =