In these probabiltiy questions I get confused wif when to use factorials, perms, combs. Is it possible do them them all with use of the Ps and Cs?
Do it logically. I did my solution logically and it worked. I can't be bothered to figuring out how they got 3!*4!*C(5,3) - but the point is 4*3*5! is the same thing.
Other students will go through their working and have 3!*4!*C(5,3) as a final answer.
But I'll go through my answer in full, so you can kinda see where I'm coming from:
1. Place a consonant in the first place... 4 ways to pick the consonant
2. Place a consonant in the last place... 3 ways
At this point we have 5 letters, 2 consonants and 3 vowels to place in 5 spots. But we don't care about whether a letter is a consonant or a vowel anymore. So we proceed as follows:
3. Pick the first consonant and place it in one of the 5 spots available... 5 ways to place it
4. Pick the second consonant and place it in one of the 4 spots available... 4 ways
5. Pick the first vowel and place it in one of the 3 spots available... 3 ways
6. Pick the second vowel and place it in one of the 2 spots available... 2 ways
7. Place the last vowel into the last spot available... 1 way
you could also say:
3. For the first available spot, pick one letter... 5 letters to pick from
4. For the next spot, pick a letter... 4 ways
(and so on)
Answer: 4*3*5*4*3*2*1 = 4*3*(5!)
So you do maths and these questions until you're comfortable. When I started out, I did my working in full like above. But then I realised
and got confident with when I was supposed to use factorials, Ps and Cs, so I started using them in my answers as a short cut.
