Modern Math

Probability

Medium

A three-digit number is chosen at random. Find the probability that its hundreds digit, tens digit and units digit are consecutive integers in descending order

1/60

1/125

2/225

7/900

✅ Correct Option: 3

Consecutive integers in descending order means each digit is exactly 1 less than the digit before it, following the pattern $(U+2,\ U+1,\ U)$ .

Listing all such three-digit numbers:

$U$	Number
0	210
1	321
2	432
3	543
4	654
5	765
6	876
7	987

$U$ cannot exceed 7 because the hundreds digit $(U+2)$ must remain a single digit $(\leq 9)$ .

Favourable outcomes $= 8$

Total three-digit numbers range from 100 to 999.

Total $= 999 - 100 + 1$

Total $= 900$

$P = \dfrac{8}{900}$

$= \dfrac{2}{225}$

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