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# restrictions combinations

+1
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In how many ways can we choose 3 distinct letters of the alphabet, without regard to order, if we must choose 1 vowel (A, E, I, O, or U) and 2 consonants?

mathtoo  Feb 18, 2018
#1
+12753
+2

Here we go....my stab at it....

5 ways to choose a vowel    a e i o u

times    21c2

5 x 21c2 = 5 x 210 = 1050 ways

ElectricPavlov  Feb 18, 2018
#2
+3039
+2

Hello, EP!

We have 5 options for the choice of the vowel, and we must make 2 choices out of the remaining 21 letters, for a total of $$\binom{21}{2} = 210$$choices for the consonants. This gives a total of $$5 \times 210 = \boxed{1050}$$.

tertre  Feb 18, 2018
#3
+12753
0

Thanx for the confirmation !

ElectricPavlov  Feb 18, 2018
#4
+3039
0

No problem, EP!

tertre  Feb 18, 2018