Question

Numbers between $1$ and $10,000$ are formed using the digits $2$ and $3$ only once and the digit $4$ twice. If the numbers thus formed are arranged in increasing order and $x, y$ represents the ranks of $4324$ and $324$ respectively then $x-y=$

• A. 17
• B. 31
• C. 14
• D. 16

Answer 1

Answer: (A)

Number between $1$ and $10000$ are formed using digit $2$ and $3$ only
one and digit $4$ twice one-digit $=\{2,3,4\}=3$
Two digit $=\{23,24,32,34,42,43,44\}=7$
Three digit number $=\{234,243,244,324,342,344$
$423,432,424,434,442,443\}=12$
Four digit number $=\{2344,2434,2443,3244,3424,3442,4234,4324 \ldots\}$
Rank of $324=14$ Rank of $4324=3+7+12+9=31$
$\therefore x-y=31-14=17$