Question

A bag contains $50$ tickets numbered $1, 2, 3, ...,50$ of which five are drawn at random and arranged in ascending order of magnitude $ ({{x}_{1}}

• A. $\frac{^{29}{{C}_{2}}{{\times }^{20}}{{C}_{2}}}{^{50}{{C}_{5}}}$
• B. $\frac{^{30}{{C}_{1}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}$
• C. $\frac{^{5}{{C}_{1}}{{\times }^{50}}{{C}_{2}}}{^{50}{{C}_{5}}}$
• D. $\frac{^{50}{{C}_{2}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}$

Answer 1

Answer: (A)

$\frac{^{29}{{C}_{2}}{{\times }^{20}}{{C}_{2}}}{^{50}{{C}_{5}}}$

Answer 2

Let E= Event of getting 5 tickets ascending order. Since, it is given that number 30 is on 3rd position. So we have to choose two numbers from 1 to 29 numbers and choose two numbers from 31 to 50
$\therefore$ $n(E){{=}^{29}}{{C}_{2}}{{\times }^{20}}{{C}_{2}}$
Total number of selection of 5 cards From 1 to 50 is,
$n(S){{=}^{50}}{{C}_{5}}$
$\therefore$ Required probability
$=\frac{n(E)}{n(S)}=\frac{^{29}{{C}_{2}}{{\times }^{20}}{{C}_{2}}}{^{50}{{C}_{5}}}$