By H. Mulholland and C. R. Jones (Auth.)
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1 (b) We now have three possible cases, namely the number of samples containing 1, 2 or 3 faulty resistors respectively. (i) Exactly one faulty resistor. e. e. 3Cl. ΤΊ = 2040 . . (ii) PERMUTATIONS AND COMBINATIONS 47 (ii) Exactly two faulty resistors. Here we pick two good resistors from 17, combined with two faulty resistors from three. Required number is 1 7 C 2 . 3 C 2 = ' -^-r = 408 . . (iii) (iii) Exactly three faulty resistors. (iv) The sum of equations (ii), (iii) and (iv) is the required answer, which 2040 + 408 4-17 = 2465 .
A) A 'true' die is thrown; calculate the expectation of the score. (b) Throw a die 60 times, noting the score. Find the mean of your results. Explain the difference between the value of the expectation obtained in (a) and the value of the mean obtained in (b). 22. If n people are allocated seats at random at a round table with n seats, what is the probability that two particular people are seated next to each other? 23. A box of 20 screws is known to contain five faulty ones. A sample of six is taken from the box.
13. Find the value of 3 0 Pi 9 . 30! No. 3 0rp 19 ~ ( 3 0 - 19)! 30! 30! 11! ~Yv. 24 = 6-346 x 10 Exercises 3c 1. (a) Evaluate 5p 6p 1 p 6 p r 3> r l Log 32-4237 7-6012 24-8225 44 ELEMENTARY PROBABILITY (b) Evaluate using log factorials 2 5 P 1 7 , 3 6 P 1 5 , 2 9 P 1 0 , 2 1 0 P 6 7 . ), 9 x 7 x 5 x 3 x 1 . 26... 2. 2. In a newspaper competition ten different motor car accessories are to be put into order of usefulness. In how many different ways can they be placed? If the entry fee was 2p per attempt and assuming sufficient entries were received to include every possible permutation once only, what was the total amount received?