JEE Advance - Mathematics (2001 - No. 5)
An unbiased die, with faces numbered $$1,2,3,4,5,6,$$ is thrown $$n$$ times and the list of $$n$$ numbers showing up is noted. What is the probability that, among the numbers $$1,2,3,4,5,6,$$ only three numbers appear in this list?
{{6{c_3}\left[ {{3^n} - 3\left( {{2^n}} \right) + 3} \right]} \over {{6^n}}}
{{6{c_3}\left[ {{3^n} - 3\left( {{2^n}} \right) + 1} \right]} \over {{6^n}}}
{{6{c_3}\left[ {{3^n} - 3\left( {{2^n}} \right) + 3} \right]} \over {{3^n}}}
{{6{c_3}\left[ {{3^n} - 3\left( {{2^n}} \right) } \right]} \over {{6^n}}}
{{6{c_3}\left[ {{3^n} - 3\left( {{2^n}} \right) + 6} \right]} \over {{6^n}}}
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