A bag contains 30 tickets numbered from 1 to 30. Five tickets are draw

1.	A bag contains 30 tickets numbered from 1 to 30. Five tickets are drawn at random and arranged in ascending order. Find the probability that the third number is 20.
Answer» Total number of ways in which 5 tickets can be drawn = n(S) = ³⁰C₅. The tickets are arranged in the form T₁, T₂, T₃ (= 20), T₄, T₅ Where T₁, T₂ ∈{1, 2, 3, …, 19} and T₄, T₅ ∈{21, 22, …, 30} ∴ Number of favourable cases = ¹⁹C₂ x 1 x ¹⁰C₂ ∴ Required probability = \(\frac{^{19}C_2\times^{10}C_2}{^{30}C_5}\) = \(\frac{19\times18}{2}\times\frac{10\times9}{2}\) x \(\frac{5\times4\times3\times2\times1}{30\times29\times28\times27\times26}\) = \(\frac{285}{5278}.\)

A bag contains 30 tickets numbered from 1 to 30. Five tickets are drawn at random and arranged in ascending order. Find the probability that the third number is 20.

Answer»

Total number of ways in which 5 tickets can be drawn = n(S) = ³⁰C₅.

The tickets are arranged in the form T₁, T₂, T₃ (= 20), T₄, T₅

Where T₁, T₂ ∈{1, 2, 3, …, 19} and T₄, T₅ ∈{21, 22, …, 30}

∴ Number of favourable cases = ¹⁹C₂ x 1 x ¹⁰C₂

∴ Required probability = \(\frac{^{19}C_2\times^{10}C_2}{^{30}C_5}\) = \(\frac{19\times18}{2}\times\frac{10\times9}{2}\) x \(\frac{5\times4\times3\times2\times1}{30\times29\times28\times27\times26}\) = \(\frac{285}{5278}.\)

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A bag contains 30 tickets numbered from 1 to 30. Five tickets are drawn at random and arranged in ascending order. Find the probability that the third number is 20.

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