Draw a card from a deck, replace it, and shuffle the deck. There are 52 equally

Question

Draw a card from a deck, replace it, and shuffle the deck. There are 52 equally likely outcomes on each draw. P (draw ace of hearts) = 1/52 is the same from draw to draw. For each of the 52 ways in which the 1st draw occurs., there are 52 ways the 2nd draw occurs. So, there are 52 times 52 ways two draws can occur. P(ace followed by ace) = 4/52 times 4/52 Outcomes without Replacement Draw a card from a deck and not replace it. P (heart) = 13/52. P (heart followed by spade) = 13/52 times 13/51 A permutation is a sequence of outcomes where outcomes are drawn without replacement and order Is important. For a sequence of n things drawn from N things without replacement, there are N ways the 1st draw occurs. For each way of the 1st trial, there are N-1 ways the 2nd trial can occur. For 2 draws, there are N x (N-1) possible ways. Continuing, there are N x (N-1) x (N-2) triples for 3 draws. in general, it's N!/(N - n)!, or = PERMUT(N, n) A combination is a group of outcomes where outcomes are drawn without replacement and order is not important. Example: How many groups of 4 can be formed from 7 people? We know there are 840 sequences possible. But 4 things can arrange themselves 4 times 3 times 2 times 1 = 4! (read 4 factorial) ways. so, there are 840/4! groups. in general, the number of combinations = the number of permutations/the number of sequences of n things = N!/(n! times (N - n)!), or = COMBIN (N, n) the number of sequences (order is important) formed by drawing without replacement of 3 things from 10 things = the number of sequences (order is important) formed by drawing with replacement of 3 things from 10 things = the number of committees of size 3 formed from 10 people =

Explanation / Answer

4. The number of sequences in order without replacement is nPk, where, n denotes number of things and k denotes number of things for selection.

Therefore, required number of sequences: 3P10=31/(10-3)!=720 (ans)

5. The number of sequences in order with replacement is n^k, where, n is number of things and k is the number of things for selection.

Therefore, required number of sequences: 10^3=1000 (ans)

6. The number of 3 member commitee formed from 10 people doesnot require any particular order to be followed. Therefore, the required sequence is nCr, where, r members to be formed in a committee out of 10 members available.

Therefore, required number is: 10C3=10!/3!(10-3)!=120 (ans)

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