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Question

Find the total number of ways of selecting five letters from the letters of the word INDEPENDENT.___


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Solution

INDEPENDENT
11 letters (3N, 3E, 2D), I, P, T = 6 types.
We have to form 5 letters - word
I. All different = 6C5.5!=(6).5!=720
II. 2 alike, 3 diff. = 3C1.5C3.5!2!
=(3.10).60=1800.
III. 3 alike, 2 diff. = 2C1.5C2.5!3!
=(2.10).20=400.
IV. 2 alike, 2 alike, 1 diff. = 3C2.4C1.5!2!2!
=(3.4).30=360.
V. 3 alike, 2 alike = 2C1.2C1.5!3!2!
=(2.2).10=40
Total selections = 6+30+20+12+4=72
Total words = 3320.


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