The number of ways in which $15$ identical gold coins can be distributed among $3$ persons such that each one gets at least $3$ gold coins is

In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

The number of ways five alphabets can be chosen from the alphabets of the word $MATHEMATICS$,where the chosen alphabets are not necessarily distinct,is equal to :

Out of $7$ consonants and $4$ vowels,the number of words consisting of $3$ consonants and $2$ vowels that can be formed is:

If $\binom{a^2+a}{3} = \binom{a^2+a}{9}$,then $a = \dots$

The number of ways $16$ identical cubes,of which $11$ are blue and the rest are red,can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes,is