21 Consider five coins labeled a b c d and e Let x number o

2.1. Consider five coins labeled a, b, c, d, and e. Let x = number of heads showing. (a) Manually count and tabulate all possible permutations for each of the following configuration s: i. x = 0 ii. x = 1 iii. x = 2 iv. x = 3 v. x = 4 vi. x = 5 Compare your results to those given by Equation (2.2). (b) Manually delete all duplicate permutations from each example of part (a), that is, cross out permutations that repeat a previous combination in a different order. Compare your results to those given by Equation (2.3).

Solution

2.1)

a)

i. x =0 : {TTTTT} ----------> Count =1

ii. x =1 : {HTTTT,THTTT,TTHTT,TTTHT,TTTTH} ----------> Count =5

iii. x =2 : {HHTTT,HTHTT,HTTHT,HTTTH,THHTT,THTHT,THTTH,TTHHT,TTHTH,TTTHH} ------> Count = 10

iv. x =3 : {HHHTT,HHTHT,HHTTH,HTHHT,HTHTH,HTTHH,THHHT,THHTH,THTHH,TTHHH} ------> Count = 10

v. x=4 : {HHHHT,HHHTH,HHTHH,HTHHH,THHHH}---------->Count =5

vi. x=5 : {HHHHH} -------> Count =1

b)

i. x =0 : {TTTTT}

ii. x =1 : {HTTTT}

iii. x =2 : {HHTTT}

iv. x =3 : {HHHTT}

v. x=4 : {HHHHT}

vi. x=5 : {HHHHH}