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
$C_{20}$
$C_{21}$
greater than $C_{21}$
less than $C_{20}$
If $^n{P_r} = 840,{\,^n}{C_r} = 35,$ then $n$ is equal to
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
A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
exactly $3$ girls $?$
The number of arrangements of the letters of the word $SATAYPAUL$ such that no two $A$ are together and middle letter is consonant, is
From a class of $25$ students, $10$ are to be chosen for an excursion party. There are $3$ students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?