The number of combinations of pins that can generated without using 19 in beginning are 3645 pins.
Given ten numbers from 0 to 9 and we are require to generate pins such that 19 will not come in beginning.
Total numbers=10
Combinations are the arrangement of numbers, variables, alphabets, etc. to form another numbers or word. In this problem we have to use combinations because there will be many combinations made from 10 numbers to form a 4 digit pin.
[tex]C=n!/r!(n-r)![/tex]
Combination: When 19 is not in beginning, we have to use 2 numbers in the beginning other than 19 so we can use all 9 numbers on thousandths place other than 1 and all the 9 numbers on hundredth place other than 9 and rest 2 places can be filled with any number from all 10 numbers so the combinations will be [tex]9 C_{1}*9C_{1}* 10C_{2}[/tex]=9*9*45=3645 pins.
Hence we can make 3645 pins of ATM from 10 numbers not starting with 19.
Learn more about combinations at https://brainly.com/question/11732255
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