I was unable to solve these 3 problems from your probability lesson, please can you help me:
3. How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used? (Ans. 1260)
I would say that it should be done as a problem where you have to find combinations of different words that can be formed from 9 letters where 3 letters A, 4 letters B and 2 letters C. In this case it should be 9!/(3!*4!*2!), but I do not fully understand a logic behind this?
2. There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group? (Ans. 80)
There are C(10,3)=120 combinations, minus combinations when there is a husband and a wife in a group of three: 5(5 different couples)*8(8 choices for one more place in a group)=40. Total 120-40=80. Is it a right approach?
7. The probability that it will rain in NYC on any given day in July is 30%. What is the probability that it will rain on exactly 3 days from July 5 to July 10 ?
There are C(5,3)=10 desired combinations of rain in 3 days and it should be 32 possible combinations if probability of rain is 1/2, but we have probability of rain as 30%, i do not know what is the next step?