I'm really sorry for posting all these questions but i really need help.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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