A child has 2 shirts (one red and one blue) and 3 types of pants (jeans, khakis, and shorts). List all the possible combinations of outfits consisting of one shirt and one pair of pants. Display your answer in a table format.
Step-by-step solution
Idea: Put the shirts down the side and the pants across the top. Each box of the table is one outfit, so the table shows every combination exactly once.
- Each of the 2 shirts can be worn with each of the 3 pants: 2 × 3 = 6 combinations.½ mark
1 markShirt ↓ / Pants → Jeans Khakis Shorts Red Red shirt, jeans Red shirt, khakis Red shirt, shorts Blue Blue shirt, jeans Blue shirt, khakis Blue shirt, shorts - So there are 6 possible outfits. As a sample space: S = {(Red, Jeans), (Red, Khakis), (Red, Shorts), (Blue, Jeans), (Blue, Khakis), (Blue, Shorts)}.½ mark
Check: Each row of the table has 3 outfits and there are 2 rows: 6 ✓. No outfit appears twice.
Answer to write in the exam
Number of outfits = 2 × 3 = 6
Table (rows: shirt; columns: pants):
Red: (Red, Jeans) | (Red, Khakis) | (Red, Shorts)
Blue: (Blue, Jeans) | (Blue, Khakis) | (Blue, Shorts)
∴ S = {(Red, Jeans), (Red, Khakis), (Red, Shorts), (Blue, Jeans), (Blue, Khakis), (Blue, Shorts)}; 6 outfits
Common mistakes that cost marks
- Adding instead of multiplying: 2 + 3 = 5 outfits. Each shirt goes with every pair of pants, so it is 2 × 3.
- Listing the 5 clothes as the answer. An outfit is a pair (one shirt and one pair of pants).
- Giving a list when the question asks for a table. Draw the table with shirts as rows and pants as columns.
How this can come in the exam
A school uniform comes in 3 shirt colours and some trouser colours, giving 12 different shirt-and-trouser combinations. The number of trouser colours is
- 4
- 9
- 15
- 36
Show answer
(A) 4
3 × (number of trouser colours) = 12, so 12 ÷ 3 = 4.
A child chooses a cap (white or black) and a pair of shoes (sports or sandals). Show all the outfits in a table. If one outfit is chosen at random, find the probability that it has a white cap and sandals.
Show answer
Table: White–Sports, White–Sandals, Black–Sports, Black–Sandals (2 × 2 = 4 outfits). Only (White, Sandals) is favourable: P = 14.Try one yourself
A child has 3 T-shirts (white, yellow, green) and 2 pairs of shorts (black, grey). How many outfits are possible? List them.
Show answer
3 × 2 = 6: (White, Black), (White, Grey), (Yellow, Black), (Yellow, Grey), (Green, Black), (Green, Grey).
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