A company has 12 eligible applicants for different committees, calculate each. a

Question

A company has 12 eligible applicants for different committees, calculate each. a. The number of ways a committee of 5 can be formed. b. The number of ways a committee of 6 with three official positions (President, Vice-President, Secretary) can be formed. If the letters R. E. D. L. E. T. T. U. C. E are all in a bag. how many total possible arrangements can be made using all the letters. If x represents the number of occupants in a randomly chosen car from the freeway, and the table gives the probability that each occurs. Find each: a. Show it is or is not a probability distribution. If it is a probability distribution find mu and sigma. Find P(more than 3) Find P(less than 4) Radioactivity decay. When studying cesium-137, it is found that over 365 days, i million radioactive atoms are reduced to 977, 287 radioactive atoms. Find each: The mean number of radioactive atoms lost in one day. Find the probability that on a given day 50 radioactive atoms decayed.

Explanation / Answer

5 a) Number of way in which a committee of 5 ca be formed out of 12 applicants = 12C5 = 12!/(5!x(12-5)!)

= 12x11x10x9x8/(5x4x3x2) = 792

B) Number of ways in which a committe of 6 with 3 official positions can be formed) = 12C6 x (6x5x4)

= 110880

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