G Tewani Solutions for Chapter: Permutation and Combination, Exercise 1: DPP

Number of four-digit positive integers, if the product of their digits is divisible by $3$ are

The number of five-digit numbers which are divisible by $3$ that can be formed by using the digits $1,2,3,4,5,6,7,8$ and $9$ when repetition of the digits is allowed is

If $\mathrm{N}$ is the number of positive integral solutions of $x_1 x_2 x_3 x_4=770$, then $\mathrm{N}=$?

I have tiled my square bathroom wall with congruent square tiles. All the tiles are red, except those along the two diagonals, which are all blue. If I used $121$ blue tiles. Then the number of red tiles I used are

The number of ordered pairs of positive integers $\left(m, n\right)$ satisfying $m\le 2n\le 60$ or $n\le 2m\le 60$ is

Number of ways in which $6$ distinct objects can be kept into two identical boxes so that the no box remains empty is

The number of four-digit numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6, 7, 8$ and $9$ such that the least digit used is $4$, when the repetition of digits is allowed, is

 A fair coin is tossed $n$ times. Let $a_n$ denotes the number of cases for which no two heads occur consecutively. Then, which of the following is not true?