Question

How many 2 letter password combinations are possible from letters A,B, C, D, E without repetition?

1) n=2, r=5, C=(2!) / ((5!) * (2-5)!)

2) n=5, r=2, C=(5!) / ( (2!) * (5-2)!)

3) n=2, r=5, C=(2+5-1!) / ((5!)*(2-1)!)

4) n=5, r=2, C=5+2-1!) / ((2!) *(5-1)!)

Answer 1

Number of 2 letter password combination are possible from letters A, B, C, D, E is the same type of problem of in how many ways 2 letter can be chosen from letters A, B, C, D, E.

[ Note: 1) We know that r letter can be chosen from n letters in ways. (Without Repetition)

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Here for this problem n = 5 and r = 2. Now applying this two formula we get, the number of 2 letter password combination are possible from letters A, B, C, D, E (without repetition) is,

Answer: Correct answer is " Option 2. "

(n=5, r=2 , C=(5!) / ((2!)*(5-2)!)