Jack packs 4 pairs of shoes, 3 pairs of boots, 7 pairs of jeans, 9 pairs of dres
ID: 3317947 • Letter: J
Question
Jack packs 4 pairs of shoes, 3 pairs of boots, 7 pairs of jeans, 9 pairs of dress pants, and 2 dress shirts for a trip. (a) How many different outfits can Jack make with these items? (b) If Jack were to bring along 3 sweaters so that he could wear either a dress shirt or a sweater or he could wear both a dress shirt and a sweater, how many outfits could Jack make? (a) Jack can make 224 different outits with these items. (Type a whole number.) (b) Jack can make 1232 different outfits with these items. (Type a whole number.)Explanation / Answer
Jack needs Shirts, Pants and Shoes
(a) Different Possible combinations He can have 1 Shirts,1 Jeans,1 Shoes or 1 shirt, 1 jeans, 1 pair of boots, or 1 shirt,1 dress pant, 1 pair of shoes or 1 shirt,1 dress pant, 1 pair of boots
= (2 * 7 * 4) + (2 * 7 * 3) + (2 * 9 * 4) + (2 * 9 *3) = 56 + 42 + 72 + 54 = 224
(b) We already have for dress shirt 224 outcomes.
Only sweater, no dress shirt = (3 * 7 * 4) + (3 * 7 * 3) + (3 * 9 * 4) + (3 * 9 *3) = 84 + 63 + 108 + 81 = 336
Both shirt and sweater (2 * 3 * 7 * 4) + (2 * 3 * 7 * 3) + (2 * 3 * 9 * 4) + (2 * 3 * 9 *3) = 168 + 126 + 216 + 162 = 672
Total Number of ways = 224 + 336 + 672 = 1232
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