How many different groups of 4 letters are possible, if exactly two vowels (not including y as a vowel) and two consonants must be among the letters selected, a letter can be used more than once, and all letters are available but the letter Q?
This is a combination question.
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We are asked for groups of letters, and so we are unconcerned with how they are arranged. Ultimately, we will have to divide by a factorial(s) of those places that can repeat.
Since order does not matter in this question, we must take into account the numbers that could repeat and remove them from the calculation. We do this by dividing by a factorial for those places that would be prone to repetition.
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The question asked us for how many groups of letters we can choose and we solved for that.