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Hi Paul,

If I have four words, ABCD, what is for the formula for the total number of combinations of 3, 2 and 1 words where the order counts ie.  BCD is different to CBD and is counted as two combinations.

Thanks for your help!

Cheers,
Usuff

Answer
Country:   New South Wales, Australia
Category:   Advanced Math
Private:   No
Subject:   Formula For Permutations
Question:   Hi Paul,

If I have four letters, ABCD, what is the formula for the total number of Permutations of 3, 2 and 1 words where the order counts ie.  BCD is different to CBD and is counted as two Permutations.

Thanks for your help!

Cheers,
Usuff
.............................
You want:

P(4,3) + P(4,2) + p(4,1) =

4 3 2 +
4 3 +
4
= 4(3 2 + 3 + 1)
= 4(3(2 + 1) + 1)

I don't have anything simpler to suggest.

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Paul Klarreich

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I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

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