Maths · Simple applications
All the five digit numbers that can be formed using the digits 1,2,3,4,5 without
All the five digit numbers that can be formed using the digits 1,2,3,4,5 without repetition, are arranged in the decreasing order of magnitude. The rank of the number 34215 is
- A. 58
- B. 62
- C. 96
- D. 128
Step-by-step solution
Total numbers formed = 5! = 120. Arranged in decreasing order. Count numbers greater than 34215:
- First digit > 3 (4 or 5): 2 choices × 4! = 48.
- First digit = 3, second digit > 4 (only 5): 3! = 6.
- First two digits = 34, third digit > 2 (only 5): 2! = 2.
- First three digits = 342, fourth digit > 1 (only 5): 1 number (34251).
Total greater = 48+6+2+1 = 57. Rank = 57+1 = 58.
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