I have four questions.

Correct answers

#21: 1/24, #23: 22/120, #24: 15/154,

#25: answer not given

#21, #24 I cannot get the correct answers.

#23

I thought it was 1 - 1/120 = 119/120

#25

I would like to make sure if it is correct.

\f21. If four fair die are rolled, what is the probability of obtaining two identical even numbers and two identical odd numbers. 23. In a neighborhood with 10 houses, k houses are not insured. A tornado randomly damages 3 of the houses. The probability that none of the damaged houses are insured is 1/120. Calculate the probability that at most one of the damaged houses is insured. 24. A professor approaches 12 undergraduate students independently, each of whom is equally likely to want to participate in research projects. Six are interested only in applied statistics research, four are interested only in actuarial science research, and two are interested only in data science research. After the talking with the students, six students state that they want to participate in the research. Calculate the probability that two participate in applied statistics research, two participate in actuarial research, and 2 participate in data science research. 25. Roll a six sided fair die. Let A be the event that the outcome on the dice is an even number. Let B be the event that the outcome on the dice is 4 or smaller. Let C be the event that the outcome on the dice is 3 or larger. a. Are A and B independent? b. Are B and C independent