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NDA 2019 Maths · Mathematics · Permutations and Combinations · medium

The number of 4-digit numbers greater than 5000 that can be formed from the digits 3,5,6,7,9 without repetition is

Single correct option

The number of 44-digit numbers greater than 50005000 that can be formed from the digits 3,5,6,7,93,5,6,7,9 without repetition is
  1. A. 120120
  2. B. 7272
  3. C. 2424
  4. D. 9696
Show answer and solution

Answer: (D) 9696

For the number to exceed 50005000, the thousands digit must be one of 5,6,7,95,6,7,9, which is 44 choices (33 is excluded). The remaining three places are filled from the four remaining digits in 4×3×2=244\times3\times2=24 ways. Total =4×24=96=4\times24=96. The value 120120 counts all 44-digit numbers, and 7272 wrongly excludes 50005000-type numbers starting with 55.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake