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Several problems of permutation and combination in senior high school mathematics
1, queuing, it must be an arrangement problem.

Senior three students line up at intervals, that is to say, between two senior three students, one seat is reserved for senior one or senior two students.

Number of permutations: a (3,3)

Senior one students have three positions to choose from: A(3, 1).

The remaining two positions are for senior two, A(2, 2).

The first senior three student has two positions to choose from, the first and the second.

So the arrangement method: A (2,2) * A (3,3) * A (3,1) * A (2,2) = 72 kinds.

2、

There are five cards in five bags of food. If you have 3 different cards, you can win the prize.

Winning probability: 3/5

3. the probability is the probability that this line is spades or hearts K.

Spades have 13, and hearts have only 1, making a total of 14.

Probability: 14/52=7/26.