Permutation Combination Question 8
Question 8 - 29 January - Shift 1
Five digit numbers are formed using the digits 1,2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1 . Then the serial number of 35337 is __________
Show Answer
Answer: 1436
Solution:
Formula: Permutation with repitition
No of 5 digit numbers starting with digit 1
$=5 \times 5 \times 5 \times 5=625$
No of 5 digit numbers starting with digit 2
$=5 \times 5 \times 5 \times 5=625$
No of 5 digit numbers starting with 31
$=5 \times 5 \times 5=125$
No of 5 digit numbers starting with 32
$=5 \times 5 \times 5=125$
No of 5 digit numbers starting with 33
$=5 \times 5 \times 5=125$
No of 5 digit numbers starting with 351
$=5 \times 5=25$
No of 5 digit numbers starting with 352
$=5 \times 5=25$
No of 5 digit numbers starting with 3531
$=5$
No of 5 digit numbers starting with 3532
$=5$
Before 35337 will be 4 numbers,
So rank of 35337 will be 1690
So, in descending order serial number will be
$3125-1690+1=1436$
