Five different letters are chosen from the word EDUCATION. How many of these choices contain at least 3 vowels?
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Five different letters are chosen from the word EDUCATION. How many of these choices contain at least 3 vowels?
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Answer:
“Education” is a nine letter word. It has five distinct vowels (a, e, i, o and u) plus four distinct consonants (c, d, t and n) in it.
If five distinct letters are chosen from them, number of choices that contain at least 3 vowels
= {(Number of ways exactly 3 vowels can be chosen from 5) * (Number of ways exactly 2 consonants can be chosen from 4)} + {(Number of ways exactly 4 vowels can be chosen from 5) * (Number of ways exactly 1 consonant can be chosen from 4)} + {Number of ways 5 vowels can be chosen from 5}
= {(5C3) * (4C2)} + {(5C4) * (4C1)} + {5C5}
= (10 * 6) + (5 * 4) + 1
= (60 + 20 + 1)
= 81.
Step-by-step explanation:
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Answer:
21 choices
Step-by-step explanation:
please correct me if i'm wrong, but this is my idea :)