Asked by TSHIRT
. 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?
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?
Answers
Answered by
mathhelper
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
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