Question

If ${}^{\prime }abcd{e}^{\prime }$ is a five digit number such that $a<b=c=d<e$, then the number of such numbers are

Answer 1

Given number $:abcde$
$\because a$ is the first digit, so $a\ne 0$
$\therefore$ Required ways = total combination of $3$ different digits from $1$ to $9$ (say $2,5,8$) out of which one digit will be repeated thrice (i.e. $25558$).
[each combinnations will give only one way]
$\Rightarrow$ Total required ways $={}^9{C}_3\times 1={}^9{C}_3=84$