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A sequence is a termary sequence, if it contains digits 0, 1 and 2. The total numbre of teranryn sequences of length 9 which either begin with 210 or end with 210, is

A

1458

B

1431

C

729

D

707

Text Solution

Verified by Experts

Since each digit in a ternary sequence of length 9 can be filled in 3 ways. Therefore, the number of nine-digit ternary sequence beginning with 210 is `3^(6)` and the number fo nine-digit ternary sequence ending with 210 is also `3^(6)`. The number of ternary sequence of 9 digits which being and end with 210 is `3^(3)`.
Thus, the total number of sequences which either begin with 210 or end with 210 is
`3^(6)+3^(6)-3^(6)=729-27=1431`
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OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Chapter Test
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  19. There are 10 points in a plane, out of these 6 are collinear. If N is ...

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