Discrete Mathematics Code Words seven letters in length are

Discrete Mathematics:

\"Code Words\" seven letters in length are to be constructed, using letters from the english alphabet. The letters in the set {a,e,i,o,u,w,y} are forbidden,so there are 19 avaiable letters.

a) How many code words are possible if repetition is permitted?

b)How many code words are possible if repetion is not permitted?

Show all work (computation,permutation)

Solution

Ans:

Since seven letters \'a\', \'e\', \'i\', \'o\', \'u\' are omitted. Total no. of remaining letters are = 19

Length of code word = 7

Hence no. of ways a group of 7 letters can be chosen from set of 19 words = ¹⁹C₇

Now, in each group of 7 letters, each letter can change its positon to give a new code word.

Hence no. of ways new code word can be made from each group = 7!

Hence total no. of possile code words are = ¹⁹C₇ x 7!