The value of ${}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}{C_3}} $ is
$^{56}{C_3}$
$^{56}{C_4}$
$^{55}{C_4}$
$^{55}{C_3}$
If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
How many numbers of $6$ digits can be formed from the digits of the number $112233$
A test consists of $6$ multiple choice questions, each having $4$ alternative ans wers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is
All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is
In how many ways can $21$ English and $19$ Hindi books be placed in a row so that no two Hindi books are together