Question:medium
If \( ^nP_4 = 5(^nP_3) \), then the value of \( n \) is equal to:
If \( ^nP_4 = 5(^nP_3) \), then the value of \( n \) is equal to:
Show Hint
A useful identity to remember is \( ^nP_r = (n-r+1) \cdot ^nP_{r-1} \). In this problem, \( ^nP_4 = (n-4+1) \cdot ^nP_3 = (n-3) \cdot ^nP_3 \). Setting this equal to \( 5 \cdot ^nP_3 \) gives \( n-3=5 \) instantly.
Updated On: May 2, 2026
- \( 5 \)
- \( 6 \)
- \( 7 \)
- \( 8 \)
- \( 9 \)
Show Solution
The Correct Option is D
Solution and Explanation
Was this answer helpful?
0
Top Questions on permutations and combinations
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- Mathematics
- permutations and combinations
- How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
- BITSAT - 2025
- Mathematics
- permutations and combinations
- A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain gluten, while the rest are gluten-free.
One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went to the same restaurant: they planned to choose two different vegetarian items and one non-vegetarian item only from the gluten-free options. The number of item combinations that Rohit and his friends could choose from, given their plan, was 12 times the number of item combinations that Bela and her friends could choose from, given their plan.
How many menu items contain gluten?- XAT - 2024
- Quantitative Ability and Data Interpretation
- permutations and combinations
- Five people are distributed in four identical rooms. A room can also contain zero people. Find the number of ways to distribute them.
- JEE Main - 2024
- Mathematics
- permutations and combinations
- Want to practice more? Try solving extra ecology questions todayView All Questions
