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) \[\frac{^{50}{{C}_{2}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}\]
Correct Answer: A
Solution :
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 \[=\frac{n(E)}{n(S)}=\frac{^{29}{{C}_{2}}{{\times }^{20}}{{C}_{2}}}{^{50}{{C}_{5}}}\]
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