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$^3{C_2} = 3$.
A person wants to climb a $n-$ step staircase using one step or two steps. Let $C_n$ denotes the number of ways of climbing the $n-$ step staircase. Then $C_{18} + C_{19}$ equals
If $^n{C_r}$ denotes the number of combinations of $n$ things taken $r$ at a time, then the expression $^n{C_{r + 1}} + {\,^n}{C_{r – 1}} + \,2 \times {\,^n}{C_r}$ equals
The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is
Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty
The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
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