How many words ( meaningful or meaningless) can be formed by using the letters of the word HOTSPOT

M4maths Previous Puzzles

10 Nov 2009 4 letter words

How many words ( meaningful or meaningless) can be formed by using the letters of the word HOTSPOT taking 4
letters at a time.

OPtion

1) 175
2) 235
3) 5040
4) 120
5) 144
6) 270
7) 72
8) 198
9) 840
10) 210

Solution

Total number of different letters = 5 ( H, O, T, S, P )
Number of Words having all the letters different = 5*4*3*2 = 120
Total number of repeated letters = 2 ( O, T )
If one letter is repeated then number of words = 2*(4*3/2)*(4*3*2*1/2)
= 144
If two repeated letters are used then number of words = 6
Total number of words = 120 + 144 + 6 = 270

Correct Option: 6 Best Solution (0)