# permutation and combination

• Dec 29th 2012, 07:16 AM
panelopy123
permutation and combination
>>2)the english alphabet contains 21 consonants and five vowels.how many strings of six lowercase letters of the english alphabet contain>a)exactly one vowel? ans:122523030>b)exactly two vowels? ans:72930375> c)atleast one vowel? ans:223149655>d)atleast two vowels?>3)how many bit strings contain exactly 8 0s and 10 1s if every 0 must be immediately followed by a 1? ans:45>4)how many bit strings of length 10 contain atleast three 1s and atleast three 0s?ans:9125) there are 6 runners in the 100-yard dash.how many ways are there for three medals to be awarded if ties are possible?(the runner or runners who finish with the fastest time receive gold medals,the runner or runners who finish with exactly one runner ahead receive silver medals, and the runner or runners who finish with exactly two runners ahead receive bronze medals).ans:873>6)how many 4-permutations of +ve integers not exceeding 100 contain three consecutive integers k,k+1,k+2 in the correct ordera)where these consecutive integers can perhaps be separarted byother integers in the permutation?ans:37927>b)where they are in consecutive positions in the permutation?ans:18915>i don't know how to solve and have exams
• Dec 29th 2012, 07:32 AM
HallsofIvy
Re: permutation and combination
Couldn't you have used spaces?

Quote:

Originally Posted by panelopy123
>>2)the english alphabet contains 21 consonants and five vowels.how many strings of six lowercase letters of the english alphabet contain>
a)exactly one vowel? ans:122523030>

b)exactly two vowels? ans:72930375>

c)atleast one vowel? ans:223149655>

d)atleast two vowels?>

)how many bit strings contain exactly 8 0s and 10 1s if every 0 must be immediately followed by a 1? ans:45>

4)how many bit strings of length 10 contain atleast three 1s and atleast three 0s?ans:9125)

there are 6 runners in the 100-yard dash.how many ways are there for three medals to be awarded if ties are possible?(the runner or runners who finish with the fastest time receive gold medals,the runner or runners who finish with exactly one runner ahead receive silver medals, and the runner or runners who finish with exactly two runners ahead receive bronze medals).ans:873>

6)how many 4-permutations of +ve integers not exceeding 100 contain three consecutive integers k,k+1,k+2 in the correct order

a)where these consecutive integers can perhaps be separarted byother integers in the permutation?ans:37927>

b)where they are in consecutive positions in the permutation?ans:18915>

i don't know how to solve and have exams

Presumably then you are taking a course in this subject! What have you learned about them? If you do not know, for example, "the fundamental counting principle", there may not be much hope for you.

"how many strings of six lowercase letters of the english alphabet contain>
a)exactly one vowel? ans:122523030>"
Okay there are 5 consonants in that string and 21 consonants. What does the "fundamental counting principle" tell you about the number of possiblities? There are
5 vowels so 5 possible values for that vowel. And, then, there are 6 places in the string that vowel could go. How many possible strings does that give?
• Dec 29th 2012, 08:24 AM
Soroban
Re: permutation and combination
Hello, panelopy123!

Quote:

2)the english alphabet contains 21 consonants and five vowels.how many strings of six lowercase letters of the english alphabet contain a)exactly one vowel? ans:122523030

we want a string of 6 letters which contains exactly one vowel.there are $_5C_1$ choices for the vowel, and $21^5$ orders
for the five consonants.then the vowel can be placed in 6 possible positions.therefore, there are: $(_5C_1)(21^5)(6) \:=\:$
$(5)(4,\!084,\!101)(6) \:=\: 122,\!523,\!030$ strings.
• Dec 29th 2012, 08:49 AM
Plato
Re: permutation and combination
Quote:

Originally Posted by panelopy123
>>2)the english alphabet contains 21 consonants and five vowels.how many strings of six lowercase letters of the english alphabet contain>a)exactly one vowel? ans:122523030>b)exactly two vowels? ans:72930375> c)atleast one vowel? ans:223149655>d)atleast two vowels?>3)how many bit strings contain exactly 8 0s and 10 1s if every 0 must be immediately followed by a 1? ans:45>4)how many bit strings of length 10 contain atleast three 1s and atleast three 0s?ans:9125) there are 6 runners in the 100-yard dash.how many ways are there for three medals to be awarded if ties are possible?(the runner or runners who finish with the fastest time receive gold medals,the runner or runners who finish with exactly one runner ahead receive silver medals, and the runner or runners who finish with exactly two runners ahead receive bronze medals).ans:873>6)how many 4-permutations of +ve integers not exceeding 100 contain three consecutive integers k,k+1,k+2 in the correct ordera)where these consecutive integers can perhaps be separarted byother integers in the permutation?ans:37927>b)where they are in consecutive positions in the permutation?ans:18915>i don't know how to solve and have exams