The numbers nCr are frequently called binomial coefficients, since they arise in
ID: 3067874 • Letter: T
Question
The numbers nCr are frequently called binomial coefficients, since they arise in the expansion of a binomial The number of ways in which r objects can be selected out of n objects is ways in which n-r objects can be selected out of n objects equal to the number of The binomial coefficients are given in Table l in Appendix B for selected values of n and r Example 1.2-9 The number of possible 5-card in hands (in 5-hand poker) drawn from a deck of 52 playing cards is Example 1.2-10 The number of possible 13-card hands that can be selected from a deck of 52 playing cards is Example1.2-11 Assume that each of the five-card hands drawn from a deck of 52 playing cards has the same probability of being selected. Then the number of possible 5-card hands that are all spades (Event A) is Think how to make the event A happen, that is how many ways that the event A can happen? How many ways we can select an all-spade five-card hand Suppose that the event B is the set of outcomes in which exactly three cards are kings and exactly two cards are queens. The number of outcomes in B is is How many ways we can select the three kings How many ways we can select the two queens Let C be the set of outcomes in which there are exactly two kings, two queens, and one jack. The number of outcomes in C is The probability of an all-spade five-card hand is The probability of the event B P(C)Explanation / Answer
The number of possible 13 card hands:
52C13=52!/13!*(52-13)!=52!/13!*39!=635013559600.