The sum of the digits at the 10^th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

The number of five digit telephone numbers having at least one of their digits repeated is

If ^a2-a \(C_2 = ^{a^2-a}\) C₄ then the value of 'a' is

The number of ways to average the letters of the word CHEESE are _________

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is _________

In how many ways 5 persons can be seated in a row?

A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?

In how many ways can the letters of the word PENCIL be arranged so that N is always next to E.

How many words can be formed using the letter A thrice, the letter B twice and the letter C thrice?

There are six periods in each working day of a school. In how many ways can one arrange 5 subjects such that each subject is allowed atleast one period?

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has at least three girls

If ¹⁰P_r-1 = 2 \(\times\) ⁶P_r, find r.

If (n + 1)C₈ : (n - 3) P₄ = 57:16, find n.

Evaluate \(\frac { (2n)! }{ n! } \)

Prove that n!(n + 2) = n! + (n + 1)!

If (n+2)! = 60(n-1)! find n.

3²ⁿ - 1 is divisible by 8

How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5 ? if
(i) repetition of digits allowed
(ii) the repetition of digits is not allowed.

If nP_r = nP_r+1 and nCr = nC_r-1 find the values of n and r.

Find r if ⁵p_r= 2⁶p_r-1