Let $n(A) = 3, \,n(B) = 3$ (where $n(S)$ denotes number of elements in set $S$), then number of subsets of $(A \times B)$ having odd number of elements, is-

In a football championship, there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included

$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 - r}{C_3} = $

All possible two factors products are formed from numbers $1, 2, 3, 4, ...., 200$. The number of factors out of the total obtained which are multiples of $5$ is

$\sum \limits_{ k =0}^6{ }^{51- k } C _3$ is equal to