21. Tingting has to perform for 12 days, and she asks Master Wang from the tailor shop to make performance clothes, and the costumes she is required to wear every day are different. If you make a shirt for 80 yuan, make a skirt or pants for 50 yuan. How much does Tingting's costume cost at least?
It's a matter of collocation, can you tell?
12=1×12,12=2×6,12=3×4,12=4×3,12=6×2,12=12×1,and (shirt) 80 yuan > (skirt or pants) 50 yuan, so the number of skirts or pants is greater than the number of shirts.
Make 1 shirt, 12 skirts or pants, 1×80+12×50=680 yuan.
Make 2 shirts, 6 skirts or pants, 2×80+6×50=460 yuan.
Make 3 shirts, 4 skirts or pants. 3×80+4×50=440 yuan.
Specific size: 440<460<680, Tingting's performance clothes need at least 440 yuan.
Tips: 3 shirts are represented by A, B, C, 4 skirts or pants are represented by 1, 2, 3, 4, there are 12 different ways to match A1, A2, A3, A4, B1, B 2, B 3, B 4, C1, C2, C3, C4.
22. Kobayashi made 3 dice, and the 6 sides of each dice were written with 2 "1", 2 "2", and 2 "3". How many different situations can occur with 3 dice at the same time and 3 numbers facing up after they fall?
The first method is to enumerate them one by one:
Teacher! There are a lot of repetitions, and the eyes are a little flowered!
Indeed, this method is simple to enumerate one by one, but it is more troublesome to remove the duplicates! The 3 data in each group of these results can be sorted from smallest to largest:
In this way, it is relatively simple to remove the duplicates, and finally there are 111, 112, 113, 122, 123, 133, 222, 223, 233, 333, a total of 10 types.
The second method is to list them one by one:
All 3 are different: 123, a total of 1 type.
2 numbers are the same: 112, 113, 122, 223, 133, 233, a total of 6 types.
3 numbers are the same: 111, 222, 333, a total of 3 types.
A total of 1+6+3 = 10 different cases.