Permutation Combination Question 16

Question 16 - 31 January - Shift 1

Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is

Show Answer

Answer: 2997

Solution:

Formula: Non-Consecutive Selection

$2++++=1296$

$\begin{matrix} 6 & 6 & 6 & 6\end{matrix} $

$3++++=1296$

6666

$40+++=216$

666

$420++=36$

66

$\underline{4} \underline{2} \underline{2}++=36$

$423++=36$

66

$424++=36$

66

$427++=36$ 66

$4290+=6$

6

$42920=1$

$42922=1$

$42923=1$

$=2997$