Theory question 115
Permutations and Combinations(a) Five (5) female and seven (7) male teachers applied for 4 vacancies in a Junior High School. The teachers are equally qualified. Find the number of ways of employing the 4 teachers. If (i) there is no restriction; (ii) at least 2 of them are females.
(b) The table shows the positions awarded to 7 contestants by Judges x and y in a competition.
Contestant: P, Q, R, S, T, U, V
Judges X: 2, 7, 1, 3, 6, 5, 4
Judges Y: 4, 6, 2, 3, 7, 1, 5
(i) Calculate, correct to one decimal place, the Spearman's rank correlation coefficient. (ii) interprete your answer in (b)(i) above.
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(a)(i) 12C4 = 495
(ii) 5C2×7C2 + 5C3×7C1 + 5C4 = 210 + 70 + 5 = 285
(b)(i) d = −2, 1, −1, 0, −1, 4, −1; Σd2 = 24
ρ = 1 − 6(24)/(7(49 − 1)) = 1 − 144/336 = 0.57 ≈ 0.6
(ii) There is a moderate positive agreement between the two judges' rankings
'At least 2 females' means 2, 3 or 4 females; add the three cases.