Search any question & find its solution
Question:
Answered & Verified by Expert
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 $x, y$ represent the ranks of 4324 and 324 respectively then $x-y=$
Options:
Solution:
1411 Upvotes
Verified Answer
The correct answer is:
17
Number between 1 and 10000 are formed using digit 2 and 3 only one and digit 4 twice
$\text { one-digit }=\{2,3,4\}=3$
$\text { Two digit }=\{23,24,32,34,42,43,44\}=7$
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 $4324=3+7+12+9=31$
$\therefore \quad x-y=31-14=17$
$\text { one-digit }=\{2,3,4\}=3$
$\text { Two digit }=\{23,24,32,34,42,43,44\}=7$
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 $4324=3+7+12+9=31$
$\therefore \quad x-y=31-14=17$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.