boloman0z

2022-06-20

How many four-digit numbers can be formed from the set $\left\{0,1,2,3,\dots ,10\right\}$ if zero cannot be the first digit and the given conditions are to be satisfied

1. Repetitions are allowed and the number must be even.
2. Repetitions are allowed and the number must be divisible by 5.
3. The number must be odd and less than 4000 with repetition allowed.

a. my solution is 2*10*10*10= 2000 because 2 is a even number and there are 10 numbers excluding 0 in set {0,1,2,3..10} and it is 4 digits that's why 2*10*10*10 b.same in letter A but 2 is changed into 5 because it must be divisible by 5 so it is 5*10*10*10=5000 c.same to A and B... Only I changed it to 3 so my solution is 3*10*10*10 = 3000

Bruno Hughes

$9\cdot 10\cdot 10\cdot 5=4500$:
Digit #1 can be any of the 9 digits in [1,2,3,4,5,6,7,8,9]
Digit #2 can be any of the 10 digits in [0,1,2,3,4,5,6,7,8,9]
Digit #3 can be any of the 10 digits in [0,1,2,3,4,5,6,7,8,9]
Digit #4 can be any of the 5 digits in [0,2,4,6,8]

$9\cdot 10\cdot 10\cdot 2=1800$:
Digit #1 can be any of the 9 digits in [1,2,3,4,5,6,7,8,9]
Digit #2 can be any of the 10 digits in [0,1,2,3,4,5,6,7,8,9]
Digit #3 can be any of the 10 digits in [0,1,2,3,4,5,6,7,8,9]
Digit #4 can be any of the 2 digits in [0,5]

$3\cdot 10\cdot 10\cdot 5=1500$:
Digit #1 can be any of the 3 digits in [1,2,3]
Digit #2 can be any of the 10 digits in [0,1,2,3,4,5,6,7,8,9]
Digit #3 can be any of the 10 digits in [0,1,2,3,4,5,6,7,8,9]
Digit #4 can be any of the 5 digits in [1,3,5,7,9]

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