Think of "P" for "permutation" and "P" for "position".
1,3,5,6,8, and 9
There are 6 things: {1,3,5,6,8,9}.
There are 4 Positions or Places to Put them:
{thousands, hundreds, tens, ones}
That's 6 things to Position in 4 places.
6 POSITION 4 = 6P4 = 6*5*4*3 = 360 such numbers:
[Start with 6, multiply by 1 less each time until
there are 4 factors. Multiply them all together.]
Explanation:
There are 6 Positions to Put the 1st number.
That leaves 5 Positions to Put the 2nd number.
That leaves 4 Positions to Put the 3rd number.
That leaves 3 Positions to Put the 4th number.
Here are all 360 4-digit numbers, 36 rows of 10 each,
computer-generated.
1256,1258,1259,1265,1268,1269,1285,1286,1289,1295,
1296,1298,1526,1528,1529,1562,1568,1569,1582,1586,
1589,1592,1596,1598,1625,1628,1629,1652,1658,1659,
1682,1685,1689,1692,1695,1698,1825,1826,1829,1852,
1856,1859,1862,1865,1869,1892,1895,1896,1925,1926,
1928,1952,1956,1958,1962,1965,1968,1982,1985,1986,
2156,2158,2159,2165,2168,2169,2185,2186,2189,2195,
2196,2198,2516,2518,2519,2561,2568,2569,2581,2586,
2589,2591,2596,2598,2615,2618,2619,2651,2658,2659,
2681,2685,2689,2691,2695,2698,2815,2816,2819,2851,
2856,2859,2861,2865,2869,2891,2895,2896,2915,2916,
2918,2951,2956,2958,2961,2965,2968,2981,2985,2986,
5126,5128,5129,5162,5168,5169,5182,5186,5189,5192,
5196,5198,5216,5218,5219,5261,5268,5269,5281,5286,
5289,5291,5296,5298,5612,5618,5619,5621,5628,5629,
5681,5682,5689,5691,5692,5698,5812,5816,5819,5821,
5826,5829,5861,5862,5869,5891,5892,5896,5912,5916,
5918,5921,5926,5928,5961,5962,5968,5981,5982,5986,
6125,6128,6129,6152,6158,6159,6182,6185,6189,6192,
6195,6198,6215,6218,6219,6251,6258,6259,6281,6285,
6289,6291,6295,6298,6512,6518,6519,6521,6528,6529,
6581,6582,6589,6591,6592,6598,6812,6815,6819,6821,
6825,6829,6851,6852,6859,6891,6892,6895,6912,6915,
6918,6921,6925,6928,6951,6952,6958,6981,6982,6985,
8125,8126,8129,8152,8156,8159,8162,8165,8169,8192,
8195,8196,8215,8216,8219,8251,8256,8259,8261,8265,
8269,8291,8295,8296,8512,8516,8519,8521,8526,8529,
8561,8562,8569,8591,8592,8596,8612,8615,8619,8621,
8625,8629,8651,8652,8659,8691,8692,8695,8912,8915,
8916,8921,8925,8926,8951,8952,8956,8961,8962,8965,
9125,9126,9128,9152,9156,9158,9162,9165,9168,9182,
9185,9186,9215,9216,9218,9251,9256,9258,9261,9265,
9268,9281,9285,9286,9512,9516,9518,9521,9526,9528,
9561,9562,9568,9581,9582,9586,9612,9615,9618,9621,
9625,9628,9651,9652,9658,9681,9682,9685,9812,9815,
9816,9821,9825,9826,9851,9852,9856,9861,9862,9865.
Edwin
