Permutations and Combinations 1 Question 3
3. The number of integers greater than 6000 that can be formed using the digits $3,5,6,7$ and 8 without repetition is
(2015 Main)
(a) 216
(b) 192
(c) 120
(d) 72
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Answer:
Correct Answer: 3. (b)
Solution:
- The integer greater than 6000 may be of 4 digits or 5 digits. So, here two cases arise.
Case I When number is of 4 digits.
Four-digit number can start from 6,7 or 8 .
Thus, total number of 4-digit numbers, which are greater than $6000=3 \times 4 \times 3 \times 2=72$
Case II When number is of 5 digits.
Total number of five-digit numbers which are greater than $6000=5 !=120$
$\therefore$ Total number of integers $=72+120=192$
