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You are given a box with 20 cards in it. 10 cards of this have the letter I printed on them. The other ten have the letter T printed on them. If you pick up 3 cards at random and keep them in the same order, the probability of making the word IIT is $\frac{K}{38} .$ The numerical value of K is

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answer is 5.

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Detailed Solution

$\frac{^{10} C_{1}}{^{20} C_{1}} \times \frac{^{9} C_{1}}{^{19} C_{1}} \times \frac{^{10} C_{1}}{^{18} C_{1}} = \frac{10 \times 9 \times 10}{20 \times 19 \times 18} = \frac{5}{38}$

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