Question

In a closet there are 10 pairs of shoes. If six shoes are selected ar random, compute the probability that among the six chosen shoes there are (a) no complete pairs (b) exactly one complete pair (c) exactly two complete pairs (d) exactly three complete pairs (e) no complete pairs and exactly three left and three right shoes.

Answer 1

* solution, given, in closet In closet Myere ore 10 pairs of Shoes. if six shoes are selected oondom ay solution.. since there shouldn't be dn't be complete pair we are allowed to choose at mostl Shoe toom each pais. therefore, our choice.com be made in fullnway - fiost choose 6 Pauts from 10 pairs in the closet, this con be done 100 ways. Thens from chosen 6 poios , choose one shoe from each this con be done ways as these are as there are two choices for each peur. Therefore, the rorcel no. of choices is 10 COX2. The no. of ways to pondomiy choose 6 shoes out of 20 is 20 ca. Therefore, 10 Ca x2 pair) = . p(no complete 2 = 2006 Scanned with CamScanner

NUE Poob that exachy one po lopaig GShows ( I pot + 4 liten 20 Shoes plexachty one pain ) locir('8C4-9) 2006 = 10 3051 387-60 306 38760 = 0.078973 c> poob. that exochorewo pour To por 20 shoes ces —— . G Shoes ( 2 paio + 2 diffon A shoe) - 1062 + (1602-8) - 2006 45+ 112 B0760 157 38760 with CS Scanned 0.004050 CS CamScanner

dy poob. that exacHY Hoee complete paio 10 pair) — 6 Shoe (:3 pwo). 20 shoes 10C4 prob = 2006 = 120 38760 -0.003095 . Scanned with CamScanner