Answer to Question #345135 in Statistics and Probability for fitre

Question #345135

Each time you visit the state fair, you play some games at the Midway. One game has four prizes (A, B, C, D). (a) How many different four letter sequences are possible if each letter is chosen from {A, B, C, D} with repeats allowed? (b) How many different four letter sequences have each letter occurring exactly once? (c) How many different four letter sequences don't contain B? (d) How many different four letter sequences have two letters, each of which occurs twice?


1
Expert's answer
2022-05-27T00:02:44-0400

a) There are "4^4=256" different four letter sequences are possible if each letter is chosen from {A, B, C, D} with repeats allowed.

b) The possible combinations, without using a letter more than once, are: "4!=24" different 4-letter sequences.

c) Different four letter sequences that don't contain B are "n^k," where n = total number of elements in a set (4)

k = number of elements selected from the set (in this case - 3)

So, "4^3=64"

d) Different four letter sequences have two letters, each of which occurs twice are:

AABB, ABAB, BABA, BBAA, AACC, ACAC, CACA, CCAA, AADD, ADAD, DADA, DDAA, BBCC, BCBC, CBCB, CCBB, BBDD, BDBD, DBDB, DDBB, CCDD, CDCD, DCDC, DDCC.

So, 24.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS