1. You are packing for a long-overdue vacation. After all the essential items ha
ID: 3041099 • Letter: 1
Question
1. You are packing for a long-overdue vacation. After all the essential items have been packed, there are still twelve clothing items on your bed that you could take on the trip (four pairs of pants, five shirts, and three pairs of socks). However, there is only room for another four pieces of clothing in your suitcase (a) How many different selections of four clothing items could be packed? b) How many selections result in exactly two pairs of pants being packed? (c) How many selections result in at least one item of each type being packed? d) You grab tour items at random, stuff them in your suitcase, and head off to the airport for your flight. What is the probability that you didn't add any socks to your luggage when randomly selecting tems for inclusion!Explanation / Answer
n =total number of clothing item = 12
pair of pants = 4
no .of shirts =5
pair of socks =12
a) Without restriction the number of different selection of 4 items could be packed = 12 C4 = 495
the number of different selection of 4 items could be packed = 495
b) two pair of pants can be selected from 4 pants in 4C2 ways = 6
and remainning 2 items can be selected from 8 items in 8C2 ways = 28
by multiplication principle
The total number of selection results in exactly 2 pairs of pants being packed = 6 *28 = 168
c) The number of possible cases to pack 4 item which contain atleast one of item of each type being packed
By addition principle
The number of selection results in atleast one item of each type being packed = 90 +120 +60 = 270
d) The number of ways to pack 4 item which not include pair of socks = ( 12- 3) C4 = 8C4 = 70
P( The pack of 4 items which not include pair of socks) = 70 / 495 = 0.1414
P( The pack of 4 items which not include pair of socks) =0.1414
Case No. Pair of pants Shirts pair of socks Number of selection 1 2 1 1 4C2 * 5C1 * 3C1 = 90 2 1 2 1 4C1 * 5C2 * 3C1=120 3 1 1 2 4C1 * 5C1 * 3C2 =60Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.