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

M4maths Previous Puzzles

26 Dec 2013 Solve

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 (2)

mahima srivastava   11 years AGO

(5c4*4!)+(2(4c2*4!/2!))+(4!/(2!*2!))=270

Like? Yes (7) | No (5)  

susmit   11 years AGO

there are following possibilities.
no. of o's : 0 0 1 1 1 2 2 2
no. of t's : 1 2 0 1 2 0 1 2
no. of ways: 24 36 24 72 36 36 36 6 : total =270
option no.6

Like? Yes (2) | No (3)