Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let $${{b_n}}$$ = the number of such n-digit integers ending with digit 1 and $${{c_n}}$$ =the number of such n-digit integers ending with digit 0.

The value of $${{b_6}}$$ is

Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let $${{b_n}}$$ = the number of such n-digit integers ending with digit 1 and $${{c_n}}$$ =the number of such n-digit integers ending with digit 0.

Which of the following is correct?

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is