Question 1: The total number of permutations is (n+m)! Boys have n! This arrangement, girls have m! In this arrangement, the calculation of girls' non-adjacent combinations is to insert the number of combinations of m individuals into the gap of n+ 1 composed of boys, that is, to choose m from n+ 1, that is. So the possibility is
Question 2: The principle of question 2 is the same as that of question 1. The difference is that people only have n gaps instead of n+ 1. To calculate the nonadjacent combination of girls is to insert the combination number of m people into the n gaps formed by boys, that is, to choose m from n, that is. So the possibility is
Probabilistic sampling is also called random sampling. Probabilistic sampling is based on probability theory and random principle, so that every unit in the group has a known non-zero probability. The probability that the whole unit is extracted can be specified by sample design and realized by some randomization operation. Although the random sample is generally not completely consistent with the population, it can calculate and control the sampling error based on the law of large numbers, so it can correctly explain to what extent the statistical value of the sample is suitable for the population, quantitatively infer the population according to the results of the sample survey, and also explain the nature and characteristics of the population to some extent. Probability sampling is mainly divided into simple random sampling, systematic sampling, classified sampling, cluster sampling and multi-stage sampling. In real life, most sampling surveys adopt the method of probability sampling to extract samples.