For the next three (03) items that follow : Five numbers are randomly picked from the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and arranged them in ascending order [\(x_1 < x_2 < x_3 < x_4 < x_5\); \(x_1\) being the smallest number and \(x_5\) being the largest number selected].
What is \(P(x_1 = 4)\) equal to?
\(\dfrac{5}{84}\)
For \(x_1=4\), the number 4 must be chosen and the other four numbers must all come from \(\{5,6,\dots,10\}\) (6 numbers). This gives \(\binom{6}{4}=15\) favourable selections out of \(\binom{10}{5}=252\) total selections, so \(P(x_1=4) = \dfrac{15}{252} = \dfrac{5}{84}\).
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