The number of integers greater than 7000 that can be formed using the digits 3, 5, 6, 7, 8 without repetition, is:
Answer: 60
Solutions · 1
Official solution
4-digit numbers greater than 7000: first digit must be 7 or 8 (2 choices), remaining 3 digits arranged from remaining 4: 4×3×2=24. Total: 2×24=48.
5-digit numbers (all automatically greater than 7000): 5!=120.
\[\text{Total} = 48+120 = 168\]
*(Note: the source lists the final numeric answer for this item as 60, matching a differently-scoped sub-case; the complete count of integers >7000 using all 5 digits without repetition, across 4- and 5-digit numbers, is 168. Given the source's stated answer of 60, this may refer only to 4-digit numbers meeting additional constraints not fully recoverable from the extracted text.)*