Chapter 1: Q.1.5 - Theoretical Exercises (page 17)

Determine the number of vectors $(x_{1}, . . . x_{n)}$ such that each $x i$ is either $0$ or $1$ and
$\sum_{i = 1}^{n} x_{i} \geq k$

Short Answer

Expert verified

The number of vectors $(x_{1}, . . . . . x_{n})$ is $144 a n d 18$

Step by step solution

Step-1 Given Information

Given in the question that,

Code is sequence of $3$ digits

The first digit is an integer between $2 a n d 9$

Second digit is either $0 o r 1$

Third digit is integer between $1 a n d 9$

we have to find the number of vectors.

Step-2 Explanation

Case (a): $3$ digit code

First digit $= 8$ options $(2 - 9)$

Second digit $= 0 o r 1 (2 o p t i o n s)$

Third digit $= 9$ options $(1 - 9)$

Total number of possible area codes will be

localid="1650010466242" $= 8 \times 2 \times 9 = 144$

Case (b):

First digit $= 1$ options $(4)$

Second digit $= 0 o r 1 (2 o p t i o n s)$

Third digit $= 9$ options $(1 - 9)$

Total number of possible area codes will be

localid="1650010663142" $= 1 \times 2 \times 9 = 18$

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Determine the number of vectors $(x_{1}, . . . x_{n)}$ such that each $x i$ is either $0$ or $1$ and
$\sum_{i = 1}^{n} x_{i} \geq k$

Short Answer

Step by step solution

Step-1 Given Information

Step-2 Explanation

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Determine the number of vectors(x1,...xn) such that each xiis either 0or 1and ∑i=1nxi≥k

Short Answer

Step by step solution

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Step-2 Explanation

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Determine the number of vectors $(x_{1}, . . . x_{n)}$ such that each $x i$ is either $0$ or $1$ and
$\sum_{i = 1}^{n} x_{i} \geq k$