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Help!!

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Problem:

English has  letters that can be vowels. This includes Y, which can be either a consonant or a vowel; for this problem, we'll consider Y a vowel.

The other  English letters are always consonants.

How many two-letter "words" can we make from these letters if we are required to use at least one vowel? (We aren't limited to words that have an actual meaning in English. Thus, for this problem, we'll include nonsense "words" like AA, QO, XY, and UZ.)

Aug 26, 2020

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Aug 26, 2020
edited by Guest  Aug 26, 2020
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What have you done so far?

Aug 26, 2020
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We can split this up into 4 cases:

CASE 1 ~ We have the variable in the front:

Since there are 6 vowels, and 20 consonants, we can multiple 6 * 20 = 120

CASE 2 ~ We have consonant in the front:

Again: 6 * 20 = 120

CASE 3 ~ Two vowels (that are the same):

Since there are 6 vowels, this will be (6 * 1) = 6

CASE 4 ~ We have 2 vowels (different):

This is 5 * 6 = 30

Add them all together, and we have: 120 * 2 + 6 + 30= 276

:)

Aug 26, 2020