Higgins was asked to make a unique three-letter arrangement using only letters from the word home. he can use each letter only once. (his arrangement doesn’t need to be a valid word.)
the probability that higgins forms a three-letter arrangement with vowels as the second and third letters is .
the probability that higgins forms a three-letter arrangement with two consecutive consonants is .

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

the first option i believe

step-by-step explanation:

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