Expert: Sherman D. - 11/19/2008

Question
Counting, Probability Distributions, and Further Topics in Probability

How many different 4-letter radio station call letters can be made

a) if the first letter must be K or W and no letter may be repeated?

b) if repeats are allowed (but the first letter is K or W)?

c) How many of the 4-letter call letters (starting with K or W) with no repeats end in R?

Answer
nCr = (n!)/(r!(n - r)!)

you have 26 letters, of which one of them has been chosen for you, so you have 25 letters. Also only the last 3 letters in the combination matter.

a.)
25C3 = (25!)/(3!(25 - 3)!)
25C3 = (25!)/(3!22!)
25C3 = 2300

however you asked if K or W was the first letter, then

2 * 2300 = 2600 radio stations

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b.)

so you have 25 letters with 3 letters that change and repeats are allowed.

25^3 = 15625

Times that by 2

31250 radio stations

http://library.thinkquest.org/20991/alg2/prob.html

although its under Permutation, it involves repeating of letters.

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c.)
This is done about like A.

you have 26 letters of which 3 have been chosen, and only the middle 2 letters matter. So this gives you 23 letters with only 2 letters changing.

23C2 = (23!)/(2!(23 - 2)!)
23C2 = (23!)/(2!21!)
23C2 = 253

times that by 2

506 radio stations.

info found at www.mathwarehouse.com/probability/combination.php