1. The English alphabet contains 26 letters, 5 of which are vowels. How many 5 letter words can be formed from the English alphabet:

a. With no restrictions

b. With no repetitions

c. Beginning with J, ending with F, and no repetitions

d. Beginning with J, ending with F, containing L, and no repetitions

e. Containing J, and no repetitions

f. Containing J and F, and no repetitions

g. Containing exactly two vowels, and no repetitions

h. Containing at most two vowels, and no repetitions

i. Containing more consonants than vowels, and no repetitions

j. With consonants and vowels alternating, and no repetitions

k. Containing exactly two L’s, and no other repetitions

l. With exactly one letter appearing exactly twice, and no other letter repeats

m. When at most one letter is allowed to repeat, and no letter appears more than twice

n. When at most one letter is allowed to repeat

o. When J appears exactly twice and F appears exactly twice

p. When exactly two letters appear exactly twice each

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1 Answer

a: no restrik is 26^5=11,881,376
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