You are looking for 7 letter strings where each character appears only once (for

Question

You are looking for 7 letter strings where each character appears only once (for example: "Barking"). The only characters allowed are the 26 letters of the alphabet, all in upper case. How many such strings contain the letters A, B, C

(a) in any order? (e.g., F B A X C V W)

(b) in correct order, but not necessarily consecuitively? (e.g, F T A X B E C)

(c) in order and consecutively? (e.g., H J A B C M D)

(d) Finally, how many such strings contain exactly one of A, B, or C somewhere in the string? (e.g., D O P B J K F)

Explanation / Answer

(a) In this case A,B,C are fixed so we have to choose rest four characters which can any 4 from rest 23. So total possibilities are 23(C)4. Now there 7 character can be permutated any, so total is:

(23(C)4)*7!

(b) Here for every 6(3!) permutation in the above case, we have only one here. So total here is:

((23(C)4)*7!)/3!

(c) Let us say we choose the starting point for A,B,C this can be 1,2,3,4,5. Now for the rest 4 we ca choose any 4 and in any order so their possibilities is 23(P)4. Total is:

(23(P)4)*5

(d) We have to choose 1 from A,B,C and 6 from rest 23 and order then in any way. So total is:

(3*(23(C)6)*7!)

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.