Question:
How many four letters words can be formed useing the letter of the words "INEFFECTIVE
Answer:
Given word is : INEFFECTIVE
T0tal number of letters = 11 in which
I-2, E-3, F-2, N-1, C-1, T-1, V-1
If we take same letters as one letter then total number of letters = 7
We have to form words which have 4 letters. Now there are following case:
1. 3 are same and 1 different letter
Total number of selection = 1* 6c1 = 6
Total number of words = (6*4!)/3! = (6*4*3!)/3! = 6*4 = 24
2. Two are alike and two are alike
Total number of words = 3c2 * {4!/(2!*2!)
= (3*24)/4
= 3*6
= 18
3. Two are alike and two are different
Total number of selection = 3c1*6c2 = (3*6*5)/(2*1) = 90/2 = 45
total number of words = 45*(4!/2!) = (45*24)/2 = 45*12 = 540
4. All letters are different
Total number of sections = 7c4 = (7*6*5*4)/(4*3*2*1) = 840/24 = 35
Toptal number of words = 35*4! = 35*24 = 840
Now
Total number of 4 letters words = 24+18+540+840 = 1422
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