Exercise 1: Counting binary strings.Count the number of binary strings of length 10 subject to each of the following restrictions.There is only one binary string of length ten with no 1's: 00000000000. There are&nbsp;210&nbsp;binary strings of length ten. Therefore the number of binary strings of length ten with at least one 1 is&nbsp;210−1.(b) The string has at least one 1 and at least one 0.(c) The string contains exactly five 1's or it begins with a 0.&nbsp;Exercise 2: Counting integer multiples.(b) How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?

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Exercise 1: Counting binary strings.Count the number of binary strings of length 10 subject to each of the following restrictions.There is only one binary string of length ten with no 1&#039;s: 00000000000. There are&amp;nbsp;210&amp;nbsp;binary strings of length ten. Therefore the number of binary strings of length ten with at least one 1 is&amp;nbsp;210−1.(b) The string has at least one 1 and at least one 0.(c) The string contains exactly five 1&#039;s or it begins with a 0.&amp;nbsp;Exercise 2: Counting integer multiples.(b) How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?

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There is at least one 1 and at least one 0 in the string. As a result, both all ones and all zeros are eliminated.&amp;nbsp;210−2&amp;nbsp;is the total amount of binary strings.&amp;nbsp;The string contains exactly 5 1s

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