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    E:\Working\Orange_Education\TouchPad_Maths_4\Open_Files\Chap_01\Chap_01
                 \ 10-Nov-2025  Bharat Arora   Proof-8                                     Reader’s Sign _______________________ Date __________

                FOrmINg NumberS

                Without repetition of Digits

                We can form many 3-digit numbers with the given digits. Let us form all the possible
                numbers using the digits 1, 5 and 4.

                                 H    T   O                      H    T   O                      H    T   O

                                 1    5   4                      5    4   1                      4    1   5
                                 1    4   5                      5    1   4                      4    5    1

                         1 in the hundreds place         5 in the hundreds place         4 in the hundreds place

                Here, 541 is the greatest  number and 145 is the smallest  number formed with the
                digits  1, 4 and 5. We see  that  the  digits  (1,  4 and 5) are in increasing  order in the
                smallest number 145 and in decreasing order in the greatest number 541.

                greatest Number

                To form the greatest number with the given digits, write the digits in decreasing order
                (descending order).
                                                                                               TTh   Th H     T   O
                example 1. Form the greatest 5-digit number using the digits
                6, 5, 0, 3 and 1.                                                                6   5    3   1   0

                Solution. We write the digits in descending order.                           greatest          smallest
                The greatest number formed with the given digits is 65,310.                    digit             digit

                Smallest Number

                To form the smallest number with the given digits, write the digits in increasing order
                (ascending order).

                example 2. Form the smallest 5-digit number using the digits 5, 8, 4, 0 and 3.

                Solution. To form the smallest number with 0 as one of the
                given digits, we write 0 at the second place from the left                      TTh  Th H     T   O
                and then write the other digits in ascending order.                              3   0    4   5    8
                The smallest number formed with the given digits is 30,458.
                                                                                             second            greatest
                With repetition of Digits                                                 smallest digit         digit

                greatest Number

                example 3. Form the greatest 5-digit number using the digits 5,                    TTh  Th H     T   O
                1, 4 and 6 by repeating the digits.
                                                                                                    6   6    5   4    1
                Solution. We repeat the greatest digit (6).
                The greatest 5-digit number formed with the given digits is 66,541.

                        16       Mathematics 4

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