Multiple choice

In how many ways the letters of the word 'PLUMBER' be arranged such that U, M always come together and P and R always come at end places?

  1. 2520

  2. 240

  3. 120

  4. 96
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Word PLUMBER (7 letters). P and R at ends: (P _ _ _ _ _ R) or (R _ _ _ _ _ P). 2 ways. Remaining letters: L, U, M, B, E. U and M must be together. Treat (UM) as one unit. We have 4 units: L, B, E, (UM). They can be arranged in 4! = 24 ways. Within (UM), 2! = 2 ways. Total = 2 * 24 * 2 = 96.

AI explanation

The word PLUMBER has 7 letters where P and R occupy the end places in 2! ways. Treating U and M as a single unit leaves 5 units to arrange, which gives 5! ways. Since U and M can switch within their unit in 2! ways, the total arrangements are 2! times 5! times 2!, equaling 2 times 120 times 2. This results in 96 ways.

Keep practicing — related questions