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Challenge Question 4

In how many ways can the number 2019 be represented as a 4-figure number, what are those representations?

Scenario 1 : When repetition of digits are allowed, we can write 2019 4-figure number in 3*4*4*4 = 192 ways.

Thousand’s place will have only 3 possible ways (2,9,1) because,  if we use 0 it will become 3-figure number.

In Hundred’s, ten’s and unit’s place we can use any digits as repetition is allowed.

T h(9,1,2) H(0,1,2,9) T (0,1,2,9) U(0,1,2,9)

Example : 9999,1209, 2221, 1192 etc

Scenario 2: when repetition is not allowed, we can write 2019 4-figure number in 3*3*2*1 = 18 different ways.

Thousand’s place value will have 3 possible options  – 2,1,9   Example: we take 9

Hundred’s place value will have 3 possible options – any of three numbers except the one used in thousand’s place. Example:  we can take any one digit other than 9 so let us take 1;91

Ten’s place value will have 2 possible options –  any one of the two numbers that are not used in thousand’s and hundred’s place. Example : we can take 2; 912

Unit’s place value will have 1 possible option – use digit that not used in above three. Example 0. ; 9120

Th (9,1,2) H(one of any 3 digits other than the one used in Th’s place) T(one of two digits other than digits used in Th’s and H’s place) U(Whatever digits is left).

2019 , 2091, 2901, 2910, 2109 ,2190

9012, 9021, 9102, 9120, 9210, 9201

1029, 1092 , 1902, 1920, 1209, 1290

Thanks.

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