Arrangements of RECOVER: How many distinct permutations of the letters in RECOVER are possible?
Aptitude
Permutation and Combination
Difficulty: Easy
Choose an option
-
A1210
-
B5040
-
C1260
-
D1200
Answer
Correct Answer: 1260
Explanation
Introduction / Context:RECOVER has repeated letters (R and E). We count distinct permutations by dividing 7! by the factorials of the repeated counts.
Given Data / Assumptions:Total letters = 7; R occurs 2 times; E occurs 2 times; others are distinct.
Concept / Approach:Distinct permutations = 7! / (2! * 2!).
Step-by-Step Solution:
7! = 5040Divide by 2! * 2! = 4 ⇒ 5040 / 4 = 1260Verification / Alternative check:Check letter counts directly: indeed two Rs and two Es.
Why Other Options Are Wrong:5040 ignores repetition; 1210, 1200 are not equal to 5040/4.
Common Pitfalls:Omitting one of the repeated-letter divisors.
Final Answer:1260