A rising number is a number in which each digit is greater than the digit to it's immediate left. These include 123 and 278... how many 3- digit rising numbers are there?
2007-10-17 13:15:30 · 3 answers · asked by Lala 3 in Science & Mathematics ➔ Mathematics
Let's think about this another way. We can't have a zero and we can't have digits repeated. So all these numbers will come from the set {1, 2, 3, ..., 8, 9}.
We need to choose 3 digits from there and then arrange them in ascending order.
This is 9 choose 3 = 9! / 3! (9-3)!
= 84 rising numbers
Let's see if we can list them...
123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138,
139, 145, 146, 147, 148, 149, 156, 157, 158, 159, 167, 168,
169, 178, 179, 189, 234, 235, 236, 237, 238, 239, 245, 246,
247, 248, 249, 256, 257, 258, 259, 267, 268, 269, 278, 279,
289, 345, 346, 347, 348, 349, 356, 357, 358, 359, 367, 368,
369, 378, 379, 389, 456, 457, 458, 459, 467, 468, 469, 478,
479, 489, 567, 568, 569, 578, 579, 589, 678, 679, 689, 789
Indeed 84 numbers!
2007-10-17 13:22:40 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
84
In the 100's there are 1+2+3+4+5+6+7=28
In the 200's there are 1+2+3+4+5+6=21
In the 300's there are 1+2+3+4+5=15
In the 400's there are 1+2+3+4=10
In the 500's there are 1+2+3=6
In the 600's there are 1+2=3
In the 700's there is 1
2007-10-17 20:33:23 · answer #2 · answered by Anonymous · 0⤊ 0⤋
I am not good at math sorry! but I can answer your question
2007-10-18 02:59:17 · answer #3 · answered by M B 1 · 0⤊ 0⤋