Question

How many words can be formed from the letters of the word "RAHUL"

• A. 6250 , 120
• B. 3125 , 240
• C. 3125 , 120
• D. 1050 , 120
  

Answer 1

The correct option is C 3125 , 120

we have to make words using the 5 letters, R, A, H, U, L.
1. If repetition is allowed - Here all the 5 letters can be repeated and can take all the 5 places.
Therefore,
Total no. of words that can be formed =
_ _ _ _ _
$\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$
5$\times$5$\times$5$\times$5$\times$5 = 3125 ways

2. If repetition is not allowed - Here no letter can be repeated after it has filled one of the 5 places.
Therefore, total no. of words that can be formed =
_ _ _ _ _
$\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$
5$\times$4$\times$3$\times$2$\times$1 = 120 ways
hence, the correct option is
C ( 3125, 120)