If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
$^{m + 1}{C_4}$
$^{m - 1}{C_4}$
$3\,.{\;^{m + 2}}{C_4}$
$3\;.{\;^{m + 1}}{C_4}$
There are two urns. Urm $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urm two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
The value of ${}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}{C_3}} $ is
Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is
The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is
There are $m$ books in black cover and $n$ books in blue cover, and all books are different. The number of ways these $(m+n)$ books can be arranged on a shelf so that all the books in black cover are put side by side is