M4maths Previous Puzzles

23 Aug 2013 Words

How many words can be formed by using 4 letters at a time of word "SURPRISE" (words may be meaningful or meaningless according to dictionary)

OPtion

1) 498
2) 510
3) 544
4) 586
5) 606
6) 642
7) 698
8) 720
9) 780
10) None of these

Solution

(1) No. of words having all letters different = 6*5*4*3 = 360
(2) No. of words having any one letter repeated
=(2*1)*(5*4*3*2*1/3*2*1*2*1)*(4*3*2*1/2*1) = 240
(3) No. of words having two letter repeated = (1)*(4*3*2*1/2*1*2*1) = 6
Total words = 360+240+6 = 606
ans 606
option 5

Correct Option: 5 Best Solution (2)

Vinay Sipani    11 years AGO

606 ways

SSRRUPIE
1st case i.e. no repetition of letters
SRUPIE => 6C2 * 4! = 360

2nd case => repetition of S
=> selection of two letters from other five letters
=> 5C2 * 4! / 2! = 120

3rd case => repetition of R
=> selection of two letters from other five letters
=> 5C2 * 4! / 2! = 120

4th case => repetition of bot S and R
arrangement of letters SSRR => 4! / (2! * 2!) = 6

=> Total ways = 360 + 120 + 120 + 6 = 606 ways

Like? Yes (16) | No (1)  

KUNAL GAURAV   11 years AGO

We have 6 distinct letters so 6P4 words can be formed from them.
We have 2 groups of 2 letters S and R. Any one of them can be selected by 2C1 and rest 2 letters can be selected from the remaining 5 letters and no. of words can be fromed is 4!/2!.
And if we select both the groups of S and R letters then we can form 4!/(2!*2!)
Finally adding all we get
6P4+(2C1*5C2 4!/2!)+4!/(2!*2!) = 606

Like? Yes (3) | No