take care of the restriction first, placing the vowels...
3XXXXXXX2
the not-used vowel is now part of the remaining 7 letters to go in the places named X
3*7*6*5*4*3*2*1*2 = ....
b) the word "selected" suggests that the order does not matter.
The one we don't want is "all 4 selected are consonants."
Number of selections without restrictions = C(9,4) = 126
number of selections with only consonants = C(6,4) = 15
No number containing at least one vowel = 126-15 = 111
. An anagram of a word is a rearrangement of its
letters. From the word “ALGORITHM”,
a) how many anagrams can be made if each
arrangement begins and ends with a vowel.
b) if four letters are to be selected, how many
these selections contained at least one vowel?
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