Combination and Permutations Question (1 Viewer)

[Saturn WY15]

How many ways can 3 vowels and 4 consonants be arranged in a row where the first and last place are occupied by consonants ?



+ Bonus Question condition that the 3 vowels have to be together and still the first and last place are occupied by consonants

 

[Carrotsticks]

Are the vowels and consonants distinct? That makes a big difference here.

 

[Saturn WY15]

What you mean by " Distinct "

 

[Carrotsticks]

What you mean by " Distinct "

Different.

ie: A, B, C and D are all distinct letters but A, A, B and C are not all distinct because we have two A's.

 

[Shadowdude]

So I'm going to assume they are all different... because that's what they usually are.

How many ways can 3 vowels and 4 consonants be arranged in a row where the first and last place are occupied by consonants ?

1. Choose a consonant to go in the first place ... 4 ways
2. Choose another consonant to go in the last place... 3 ways
3. We have 3 vowels and 2 consonants left to fill in the remaining 5 places. Arrange them... 5! ways

Answer: 5!*4*3 = 1440.

+ Bonus Question condition that the 3 vowels have to be together and still the first and last place are occupied by consonants

1. Choose a consonant to go in the first place ... 4 ways
2. Choose another consonant to go in the last place... 3 ways
3. Consider the 3 vowels as taking up one 'place'. Choose a 'place' for it to go... 3 ways
4. Arrange the 3 vowels in the 'place'... 3! ways
5. We have two remaining consonants, arrange them in the remaining two places... 2! ways

Answer: 4*3*3*3!*2! = 432


Think that's right.

 

[Saturn WY15]

yeah the first one is right and the second one i made up but seems to be right

 

[Saturn WY15]

Thanks everyone