interview IIsc

Question

Given a deck of 10 cards numbered 1 to 10. Select 3 cards one by one. Find the probability that selected cards is in increasing order. Eg : {1, 5, 7} or {8, 9, 10} etc

Comments

Total outcomes $= 10*9*8$
Favourable outcomes $= \binom{10}{3}$  (Choosing 3 cards out of 10 cards. Now they can be arranged in just 1 way i,e in increasing order)
$Probability= \frac{\binom{10}{3}}{10*9*8} = \frac{\Large\frac{10*9*8}{3*2*1}}{10*9*8} =\frac{1}{6} = .166$

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The card needs to be selected = 3

Total number of arrangement with these = 3!= 6

Since only 1 permutation leads to ascending order so, probability = 1/6