2. +-8 points My Notes Ask k Your Teacher Peg has 4 long-sleeve shirts, 7 short-
ID: 3145956 • Letter: 2
Question
2. +-8 points My Notes Ask k Your Teacher Peg has 4 long-sleeve shirts, 7 short-sleeve shirts, and 5 pairs of pants (a) How many different ways can Peg dress (assuming she is going to wear a shirt and a pair of pants)? (b) Peg is going on a trip to visit a friend and plans to take 3 shirts and 2 pairs of pants. How many possibilities are there for the articles of clothing she chooses to pack? (c) Peg is going on a trip to the mountains and plans to, again, take 3 shirts and 2 pairs of pants, but since it is supposed to be chilly she decides that the shirts she takes should all be long sleeve. How many possibilities are there for the articles of clothing she chooses to pack? (d) Peg is going on a business trip and plans to, again, take 3 shirts and 2 pairs of pants. This time she decides that of the shirts she takes AT LEAST ONE should be a long sleeve shirt. How many possibilities are there for the articles of clothing she chooses to pack?Explanation / Answer
given
long sleeve shirts = 4
short sleeve shirts =7
pair of shorts = 5
a) total shirts = 4+7 =11
no of ways we choose dress =11c1*5c1 = 11*5 = 55
b) peg choose 3 shirt s and 2 pair of pants
total possiblities = 11c3*5c2 = 165*10 = 1650
c) 3 long sleeve shirts and two pair of pants
total poosibilities =4c3*5c2 =4*10= 40
d) atleast one should be long sleeve shirt
There are 3 cases:
1 long sleeve + 2 pants: there are C(4,1)C(5,2) = 4x10 = 40ways
2 long sleeves + 2 pants: there are C(4,2)C(5,2) = 6x10= 60 ways
3 long sleeves + 2 pants: there are C(4,3)C(5,2)= 4x10 = 40 ways
In total, there are 40+60+40= 140 ways
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