Permutations & Combinations
Rank of a number in descending order
nta_pyq_2023_jan
Grade 11
Question:
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 _____.
Step-by-Step Solution
Key Concept: Find rank of 35337 in ascending order, then compute descending rank using total count.
Numbers before 35337 in ascending order: starting with 1 or 2 = 625+625=1250; starting with 31,32,33 = 125$\times$3=375; starting with 351,352 = 25+25=50; starting with 3531,3532 = 5+5=10; starting with 35331,35332,35333,35335 = 4. Ascending rank = 1690. Descending serial = 3125−1690+1 = 1436.
Correct Answer: 1436