How many words can be formed by using 5 letters of the word UMBRELLA at a time

M4maths Previous Puzzles

29 Sep 2011 Umbrella

How many words can be formed by using 5 letters of the word UMBRELLA
at a time

OPtion

1) 4260
2) 4220
3) 2640
4) 2460
5) 6240
6) 6420
7) 4460
8) 4640
9) 2660
10) none of these

Solution

Words having all the letters different = 7*6*5*4*3*2*1/2*1 = 2520
Words having repetition of l = [7*6*5*4*3*2*1/(3*2*1)(4*3*2*1)]*[5*4*3*2*1/2*1] = 2100
so total methods = 2520 + 2100 = 4620

Correct Option: 10 Best Solution (4)