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The number of ways in which we can selec...

The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is a. `27378` b. `27405` c. `27399` d. none of these

A

27378

B

27405

C

27399

D

none of these

Text Solution

Verified by Experts

The numbre of ways of selecting any four numbres from 1 to 30, is `""^(30)C_(4)`. Four consecutive numbers can be chosen in the following ways : (1, 2, 3, 4),(2, 3, 4, 5),…….,(27, 28, 29, 30). Thus, required number of ways `=""^(30)C_(4)-27=27378`.
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