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How many words,with or without meaning, each of 3 vowels and 2 consonants canbe formed from the letters of the word INVOLUTE?

 Jan 31, 2021
 #1
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Since there are 3 vowels, we don't have to choose those.

There are 5 consonants, and we have to choose 2. For now, the order doesn't matter, so 5*4/2=10 ways to choose.

So we have to order five distinct items.

There are 5 possibilities for the first letter of the word, 4 for the next, 3 for the middle, 2 for the second-to-last, and only 1 remaining for the last slot.

so 5*4*3*2*1=120. 

10 ways to choose the letters times 120 ways to order those letters =1200 possible words.

 Jan 31, 2021
 #2
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...uhhh..... there are FOUR vowels......

                       and there are FOUR consonants ......

Guest Jan 31, 2021
 #3
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im an idiot... i probably should have known LNVOLUTE wasn't a word...

3 out of 4 would be 4 combinations

2 out of 4 would be 6 combinations

4*6=24

24*120=2880

 Jan 31, 2021

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