In how many ways 9 pictures can be hung from 6 pictures nail on a wall?

If ²ⁿC₃ : ⁿC₂ = 44 : 3, find n

Find r if ⁵⁴P_r+3 : ⁵⁴P_r+3 = 30800 : 1

If ⁿC₅ and ⁿC₄ are in A.P. then find n.

If ⁿC _r-1=36, ⁿC_r = 84 and ⁿC_r+1 = 126 then find ^rC₂

\(\text{If } \frac { (n-1)! }{ n-4)! } :\frac { n! }{ (n-4)! } =1:9\) find the value of n

Evaluate:\(\frac { 15! }{ 9!5! } \)

If \(\frac { (n-1)! }{ (n-4)! } :\frac { n! }{ (n-4)! } \) = 1:9, find the value of n

In how many ways can 5 letters be posted in 4 letter boxes?

How many three digit odd numbers can be formed by using the digits 1,2,3,4,5 and 6 if (i) the repetition of digits is not allowed. (ii) the repetition of digits is allowed.

A man wants to select a shirt and trousers from a showroom. If there are 20 shirts and 50 trousers in variety, in how many ways can he choose one shirt and one trousers?

How many different words can be formed with the letters of the word SUNDAY? How many of these begin with N? How many begin N and end in Y?

How many words can be formed out of the letters of the word 'ORIENTAL' so that the vowels occupy the odd places?

How many 3 digit numbers more than 600 can be formed by using the digit 2, 3, 4, 6 and 7.

How many 4-digit numbers are there, when a digit may be repeated any number of times?