If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is
$8$
$3$
$5$
$2$
(b) $^8{C_r}{ = ^8}{C_{r + 2}}$
$\Rightarrow 8 – r = r + 2 $
$\Rightarrow r = 3$
Hence$^3{C_2} = 3$.
In a conference of $8$ persons, if each person shake hand with the other one only, then the total number of shake hands shall be
If $x,\;y$ and $r$ are positive integers, then $^x{C_r}{ + ^x}{C_{r – 1}}^y{C_1}{ + ^x}{C_{r – 2}}^y{C_2} + …….{ + ^y}{C_r} = $
If the number of five digit numbers with distinct digits and $2$ at the $10^{\text {th }}$ place is $336 \mathrm{k}$, then $\mathrm{k}$ is equal to
$^n{P_r}{ \div ^n}{C_r}$ =
It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?
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