SOLUTION: how many three digit numbers have only even digits?
How many ways are there to rearrange the letters in the word aptitude,if the first and last letter must each be a vowel?
Question 321453: how many three digit numbers have only even digits?
How many ways are there to rearrange the letters in the word aptitude,if the first and last letter must each be a vowel? Found 2 solutions by galactus, Edwin McCravy:Answer by galactus(183) (Show Source): You can put this solution on YOUR website! There are 4 even digits: 2,4,6,8
There are 4 choices for the first place, the second place, and the third place
4*4*4=64 three digit numbers that have all even digits.
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There are 4!/2!=12 ways to place the vowels on the ends:
ae,ai,au,ea,ei,eu,ia,ie,iu,ua,ue,ui
Place them and arrange the 6 inside letters in 6!/2! ways.
We divide by 2 because of the repeated 't'.
So, the number of ways is 12*(6!/2!)=4320 ways Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
We can choose the 1st digit as 2,4,6, or 8. That's 4 ways.
We can choose the 2nd digit as 0,2,4,6, or 8. That's 5 ways.
We can choose the 3rd digit as 0,2,4,6, or 8. That's 5 ways.
Answer 4*5*5 = 100 three-digit numbers with only even digits.
Edwin