X) How many different eleven-letter words (not necessairly pronounceable or meaningful) can be made from the letters in the word MISSISSIPPI?

ANS:

11!/4!4!2!

X) How many different 5-card poker hands can be dealt from a regular 52 card deck?

ANS:

52 C 5

XII) How many of these hands contain no aces?

ANS:

48 C 5

XIII) How many contain n aces for n = 0 to 4

ANS:
0 ==> 48 C 5
1 ==> 4C1 * 48C4
2 ==> 4C2 * 48C3
3 ==> 4C3 * 48C2
4 ==> 4C4 * 48C1



5)

Find P(F(complement)G(complement)H), given the following:
P(F) = .7 , P(G) = .6 , P(H) = .5, P(FG) = .4, P(FH) = .3, P(GH) = .2, P(FGH)=.1

ANS:

P(F(complement)G(complement)H) = P(H) - P(HF) - P(HG) - P(FGH)
= .5 - .3 - .2 + 0.1
= .1



6)

All the answers are correct.

Thanks Vinux! I really appreciate it. I have one more question if you don't mind.


A box contains tickets marked 1,2,3,....n. Find the probability of drawing a second number that is bigger than the first number. Assume Sampling Without Replacement.

I don't have an answer personally, but I'd appreciate some help.

0.5 is the answer, using rule of unbiased principle ( if you wanted ot calculate mathematicall y then hint: consider nP2 combination)

The total ways in which 2 no.s can be selected ( without replacement) from 'n' no.s is n*(n-1).
first no.is 1 then desired ways ( second no. more than first) are (n-2)
first no.is 2 are (n-3) & so on.
Hence desired no. of ways is Sum (n-2)+(n-3)+(n-4)+....3+2+1.
That is ( n(n-1) -(n-1)(n)/2 ) /n(n-1) =1/2.