A) \[\frac{1}{\sqrt{2}}\]
B) \[\frac{1}{2}\]
C) \[1\]
D) \[\frac{1}{3}\]
Correct Answer: C
Solution :
The number of ways of selecting any four numbers from 1 to 30 is\[^{30}{{C}_{4}}\]. Four consecutive numbers can be chosen in the following ways. \[(1,2,\text{ }3,\text{ }4);\text{ (}2,\text{ }3,\text{ }4,\text{ }5);\text{ (}3,\text{ }4,\text{ }5;\text{ }6);\] \[...\text{ }(27,28,29,30)\] ie, the number of ways of selecting four consecutive numbers is 27. Thus required number of ways \[{{=}^{30}}{{C}_{4}}-27=\frac{30.29.28.27}{4.3.2.1}-27\] \[=27405-27=27378\]
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