Surname from the First

Probability Level 3

How many total possibilities are there to form a surname from the letters in $CALVIN$ , using each letter at most once?

Details and assumptions:

Order matters for forming the surname. For instance, $AV$ is not the same as $VA$ .
The surname must contain at least one letter.

The answer is 1956.

1 solution

Michael Huang
Jan 26, 2017

Let $n$ denote the nonzero number of letters chosen from the first name. Since there are $6$ distinct letters, there are $\dbinom{6}{n}$ ways to choose from. Then, there are $n!$ ways to rearrange the letters for the surname. Thus, $\sum\limits_{n=1}^{6} n! \dbinom{6}{n} = \boxed{1956}$

If you mess around with that type of sum, you can rewrite it as [6!*e]-1 (we subtract 1 to remove the empty name)

Brian Moehring - 4 years, 4 months ago

Yes, that is another way to express the number. :)

Michael Huang - 4 years, 4 months ago

Surname from the First

The answer is 1956.

1 solution

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