Consider all 5 letter "words" made from the full english alphabet. (a) how many of these words are there total? (b) how many of these words contain no repeated letters? (c) how many of these words start with an a or end with a z or both (repeated letters are allowed)?

a) There are 11,881,376 of these words in total.

b) 7,893,600 of these words contain no repeated letters.

c) 896,376 of these words start with an a or end with a z or both.

Step-by-step explanation:

The English alphabet has 26 letters.

Our word has the following format

C1 - C2 - C3 - C4 - C5

C1 is the first character, C2 the second, etc...

(a) How many of these words are there total?

Each of C1, C2,... can be 26. So the total is

There are 11,881,376 of these words in total.

(b) How many of these words contain no repeated letters?

C1 can be any letter. C2 can be any letter bar the letter at C1. C3 any other than C2, C1... So

26-25-24-23-22

7,893,600 of these words contain no repeated letters.

(c) How many of these words start with an a or end with a z or both (repeated letters are allowed)?

Start with a, end with any letter other than z.

1-26-26-26-25

End with z, start with any other letter than A

25-26-26-26-1

Start with A, end with Z

1-26-26-26-1

896,376 of these words start with an a or end with a z or both.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.