A manufacturer is studying the effects of cooking temperature, cooking time, and

Question

A manufacturer is studying the effects of cooking temperature, cooking time, and type of cooking oil for making potato chips. Three different temperatures, 4 different cooking times, and 3 different oils are to be used. (a) What is the total number of combinations to be studied? (b) How many combinations will be used for each type of oil? (c) Discuss why permutations are not an issue in this exercise. Consider the situation in number 3, and suppose that the manufacturer can try only two combinations in day. (a) What is the probability that any given set of two runs is chosen? (b) What is the probability that the highest temperature is used in either of these two combinations?

Explanation / Answer

3)

temperature - 3

cookin time - 4

oil - 3

a) 3 *4 *3 = 36

b) 3 *4 = 12

4) a) total number of ways of selcting two combination = 36C2 = 36*35/2

hence required answer = 2C2 / 36 C2 = 1/ 36C2 = 2/(36*35) =0.001587301

b)   

number of ways in which highest temperature is there = 12 C 2 = 12*11/2

as there are 4 type of cookin time and 3 type of oil

hence 4*3 and we have to choose 2 out of 12

required answer

= 12 C2 / 32C2 = 12*11 /(32*31) = 0.133064

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