In a high school, a committee has to be formed from a group of 6 boys M₁, M₂, M₃, M₄, M₅, M₆ and 5 girls G₁, G₂, G₃, G₄, G₅.

(i) Let $$\alpha $$₁ be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.

(ii) Let $$\alpha $$₂ be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.

i) Let $$\alpha $$₃ be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.

(iv) Let $$\alpha $$₄ be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls such that both M₁ and G₁ are NOT in the committee together.

LIST-I	LIST-II
P. The value of $\alpha_1$ is	1. 136
Q. The value of $\alpha_2$ is	2. 189
R. The value of $\alpha_3$ is	3. 192
S. The value of $\alpha_4$ is	4. 200
	5. 381
	6. 461

The correct option is

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

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