Question:
The number of integers greater than $6,000$ that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is
The number of integers greater than $6,000$ that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is
Updated On: Feb 14, 2025
- 216
- 192
- 120
- 72
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The Correct Option is B
Solution and Explanation
$6 / 7 / 8$
$----$
$\downarrow$
$3 \times{ }^{4} C_{3} \times 3 !=72$
$-----\,\,\,=120$
Total $=192$
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects