3U Combinations Q (1 Viewer)

[Mathematician]

I need help with this problem. Im so bad at cominations and just decided to do 5 q's to see how they are. I cant do the first one.

Q

In how many ways can 4 consonants and 3 vowels be arranged in a row so that the first and the last places are occupied by consonants.

 

[ND]

It's basically asking you how many ways 2 consonants and 3 vowels can be arranged (multiplied by 2).

 

[Mathematician]

..

Answer is 1440

So theres more to it. I did what u thought -- > didnt get right answer.

 

[McLake]

21*5*4*3*20*19*18*17*4!*2 if unique

21*5*5*5*21*21*21*4!/2!*3! if not unique

Is this right?

EDIT: I am tottaly wrong, I hate prob ...

 

[Archman]

there are 4 ways of picking the starting letter and 3 to pick the ending. For the in between ones, its just as usual: 5!, so its 4*3*5! = 1440

 

[-=«MÄLÅÇhïtÊ»=-]

Yup
or more systematically, this is the type where you select your combinations and then permutate.

pick 2 Cs to be satisfy condition = 4C2
this can be arranged in 2 ways so *2

the remaining 5 can be arranged in any way, so 5!

4C2*2*5! = 1440

 

[Mathematician]

...

Thanx guys, i get it now