Peg has 4 long-sleeve shirts, 6 short-sleeve shirts, and 6 pairs of pants. (a) H

Question

Peg has 4 long-sleeve shirts, 6 short-sleeve shirts, and 6 pairs of pants. (a) How many different ways can Peg dress (assuming she is going to wear a shirt and a pair of pants)? 60 (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? 1800 (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 artidles of clothing she chooses to pack? 150 (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? 150 3. 4/7 points | Previous Answers My Notes Ask Your Teacher Ellen must take 4 courses this semester. She has a list of 4 math courses and 6 science courses to from which to choose 210 (a) Initially Ellen is under the impression that she can simply take any four of the courses on the list. If this was the case, how many different ways could Ellen select the four courses? (b) Ellen's boyfriend tells her that he thinks that she must choose 2 math courses and 2 science courses to meet her degree requirements. If this is true, how many different ways can she select the four courses? 90 (c) Ellen's speaks to her advisor and finds out that her program actually only requires that at least one of her four courses be a math course. Knowing this, how many different ways can she select the four courses? 80

Explanation / Answer

(C)

There are 4 full sleeves shirts so number of ways of selecting 3 shirts out of 4 shirts is

C(4,3) = 4

There are 6 pair of pants so number of ways of selecting 2 pair out of 6 pants is

C(6,2) = 15

So the requried number of ways is 15 *4 = 60

(d)

Total number of ways of selecting 3 shirts and 2 pair of pants is 1800

Number of ways of selecting only 3 short sleeves shirts and 2 pair of pants is C(6,3) *C(6,2) = 300

Hence, possible number of ways of selecting at least one long sleeves shirt is

1800 - 300 = 1500

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3:

(c)

Number of ways of selecting all science courses is C(6,4) = 15

Total number of waus of selecting 4 courses out of 4+6 = 10 courses is 210 (from part a)

So possible number of ways of seelcting at least one math course is 210 - 15 = 195

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