Permutations & Combinations
Counting integers greater than a value without repetition
nta_pyq_2023_jan
Grade None
Question:
The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition, is
Step-by-Step Solution
Key Concept: Count 4-digit numbers > 7000 and all 5-digit numbers separately.
4-digit numbers > 7000: first digit 7 or 8 (2 choices) $\times$ 4 $\times$ 3 $\times$ 2 = 48. 5-digit numbers: 5! = 120. Total = 120 + 48 = 168.
Correct Answer: 2