How many ways n distinct objects be placed in 2 different boxes so that no box remains empty?

In how many ways 5 different balls can be distributed into 3 boxes so that no box remains empty ?

Statement 1: let E={1,2,3,4}a n dF={a ,b} Then the number of onto functions from EtoF is 14. Statement 2: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

In how many ways can 2t+1 identical balls be placed in three distinct boxes so that any two boxes together will contain more balls than the third?

The number of ways in which 6 different balls can be put in two boxes of different sizes so that no box remain empty is :

Five balls of different color are to be placed in three boxes of different size. Each box can hold all five. In how many different ways can we place the balls so that no box remains empty?

In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together?

In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together ?

A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can be letters be placed in the envelopes so that all the letters are in the wrong envelopes.

In how many ways can 5 different subjects be arranged in 6 periods of a class?

In how many ways can a person post 5 letters in 4 letters boxes ?