First slide

Combinations

Question

The number of ways selecting three numbers from 1 to 30, so as to exclude every selection of three consecutive number is:

Moderate

A

4030
B

4031
C

4032
D

4035

Solution

The numbers of ways of selecting 3 number our of 30 is $^{30} C_{3}$ . But this include 28 ways of selecting 3 consecutive numbers. [viz (1, 2, 3), (2, 3, 4), 3, 4, 5),……,(28, 29, 30)]
Thus, required number of ways is $^{30} C_{3} - 28 = 4032$ .

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