The diagram below shows the keypad for an automatic teller machine. As you can see, the same sequence of keys represents a variety of different strings. For instance, 2133 represents AZDE and BQFD. 1 3 QZ АВС DEF 4 6 GHI JKL MNO 7 8 PRS TUV WXY (a) How many different strings are represented by the same sequence of keys for 1234? (b) At a particular bank, each debit card is assigned a PIN number. This is a four-digit numeric sequence that does not contain a 1 or a 0. How many possible PIN numbers are there? (c) How many different strings are represented by all of the available PIN numbers? (assume a PIN number is 4 digits and does not include a 1 or a 0)

The diagram below shows the keypad for an automatic teller machine. As you can see, the same sequence of keys represents a variety of different strings. For instance, 2133 represents AZDE and BQFD. 1 3 QZ АВС DEF 4 6 GHI JKL MNO 7 8 PRS TUV WXY (a) How many different strings are represented by the same sequence of keys for 1234? (b) At a particular bank, each debit card is assigned a PIN number. This is a four-digit numeric sequence that does not contain a 1 or a 0. How many possible PIN numbers are there? (c) How many different strings are represented by all of the available PIN numbers? (assume a PIN number is 4 digits and does not include a 1 or a 0)

Name: The diagram below shows the keypad for an automatic teller machine. A
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Description: The diagram below shows the keypad for an automatic teller machine. As you can see, the samesequence of keys represents a variety of different strings. For instance, 2133 represents AZDE and BQFD.123QZАВСDEF45GHIJKLMNO789.PRSTUVWXY(a) How many diffe

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

The diagram below shows the keypad for an automatic teller machine. As you can see, the same
sequence of keys represents a variety of different strings. For instance, 2133 represents AZDE and BQFD.
1
2
3
QZ
АВС
DEF
4
5
GHI
JKL
MNO
7
8
9.
PRS
TUV
WXY
(a) How many different strings are represented by the same sequence of keys for 1234?
(b) At a particular bank, each debit card is assigned a PIN number. This is a four-digit numeric sequence
that does not contain a 1 or a 0. How many possible PIN numbers are there?
(c) How many different strings are represented by all of the available PIN numbers?
(assume a PIN number is 4 digits and does not include a 1 or a 0)

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