I'm really sorry for posting all these questions but i really need help. 1. Show that C 2(2n-1, n-1) = C (2n, n) Heres what i did. 2 x (2n-1)!/2n-1-n-1)!(n-1)! = 2n!/n I dont know how to get the LS to equal the RS. 2. Determine the probability of each of the following. a) a five card poker hand dealt from a standard deck of 52 playing cards results a full house (3 of a kind and 2 of a kind) b)Two face cards are drawn in a row (w/o replacement) from a standard deck of 52 playing cards given that the first card is a king. c) a committee of 6 people randomly chosen from seven males and eight females is either all male or female d) in a six person sprint, Jessie finishes first, Marnie second and Raul last. Heres what i did. a)52!/3! x 2! but i think thats wrong. then i did 5 over that total but they have 6 as a numerator and i cant get that. b)this one i dont kno how to do. c) C(7,0) + C (8,0) Is that right? 3. Use the appropriate counting techniques a)In how many permutations of the digits 123456789 are the number 1 and 2 beside each other. b)A school has 480 girls and 520 boys. How many committees of 5 members can be formed if there must be atleast 1 boy on each committe. c) How many groups consisting of at least 2 people can be chosen from a group of 10 people. a) P(9,2) again its not right and i dont know what to do b) C (480,4) x C (520, 1) + C (480, 3) x C (520, 2) + C (480,2) x C (520, 3) + C (480, 1) x C (520, 4) + C (480,0) x (520, 5) I think im totally off on this one. c) 10!/(10-2)! Is this right? Again sorry for all these questions but i really need to understand this.