Question

7 4. Solve the recurrence an -Tan-1+10an-2 16n, subject to the initial conditions ao 5 and a1 4. li) a) How m any words can be made by rearranging all thirteen letters of TO BE OR b) How many of the words found in a) consist of six vowels followed by seven conso- ii) Four friends called Julia, Tony, Wayne and Joe are playing a hand of bridge. A standard a) Find the probability that the cards dealt to Julia and Wayne include all thirteen b) Find the probability that the cards dealt to Julia and Wayne include at least one NOT TO BE? nants? pack of 52 cards is dealt out, 13 cards being given to each player. spades. complete suit (that is, thirteen spades, thirteen hearts, thirteen diamonds or thirteen clubs). iv) A sum of S111 is to be distributed among eight people. In how many ways can this be done: a) if each person receives a whole number of dollars (that is, S0, $1, $2,...)? b) if each person receives a multiple of 5 cents (that is, S0.00, $0.05, $0.10,..., $0.95, $1.00, $1.05,...)? c) if each person receives a whole number of dollars, and no-one receives more than $15?

question3 I am not sure about this question can anyone give a very detailed solution for this?

Answer 1

(a) Total no. of cards dealt to Julia and Wayne (combined)

= 13 + 13 = 26

26 cards can be selected out of the standard deck of 52 cards in 52C26 ways

Now, if the cards dealt to Julia and Wayne needs to include all the 13 spades, only 13 cards need to be selected out of the remaining 39 cards

Thus can be done in 39C13 ways

Required probability = 39C13/52C26 = 0.0000164

(b) This case is similar to (a) just with a difference that a suit needs to be selected out of 4 suits of which all the 13 cards are dealt to Julia and Wayne. This can be done in 4 ways.

Thus, the required probability = 4*0.0000164 = 0.0000656