3,4四个数字可以组成数字不重复和自然数的个数是多少?
用1,2,3,4四个数字可以组成数字不重复和自然数的个数是多少?
你的问题不是很清楚,如果是要求组成的四位数中的每个数字都不重复的个数是:4*3*2*1=24个(比如1234 2341这种组合) 如果是组成的四位数中允许个别数字是重复的但是所有的四位数的值不相同就可以,那么可以组合成的个数4*4*4*4=256个。(比如2214与1422,这个两个四位数的值不相同,但是组成他们的数字的是有不同程度的相同) 另外,你有没有对位数要求,因为在允许某些位数相同的情况下,1 2 3 4还可以组成五位数或者六位数甚至更高的位数。
一位数:1,2,3,4, (4个) 二位数:|12,13,14, (12个)|21,23,24, |31,32,34, |41,42,43, 三位数:|123,124,132,142, (16个)|213,214,231,234 |312,314,321,324 |412,413,421,423 四位数:|1234,1243,1324,1342,1423,1432 (24个)|2134,2143,2341,2314,2413,2431 |3124,3142,3214,3241,3412,3421 |4321,4312,4123,4132,4213,4231 以上是不重复的数,一共56个 再加上可重复的自然数: 二位数:11,22,33,44(4个) 三位数:|111,121,122,131,133,141,144, (28个) |222,211,212,232,223,242,224, |333,313,331,323,332,343,334, |444,414,441,424,442,434,443, 四位数:|1111,1112,1113,1114, ( |1121,1122,1123,1124, |1131,1132,1133,1134, |1141,1142,1143,1144, |1211,1212,1213,1214, |1221,1222,1223,1224, |1231,1232,1233,1234, |1241,1242,1243,1244, |1311,1312,1313,1314, |1321,1322,1323,1324, |1331,1332,1333,1334, |1341,1342,1343,1344, |1411,1412,1413,1414, |1421,1422,1423,1424, |1431,1432,1433,1434, |1441,1442,1443,1444, |2111,2112,2113,2114, |2121,2122,2123,2124, |2131,2132,2133,2134, |2141,2142,2143,2144, |2211,2212,2213,2214, |2221,2222,2223,2224, |2231,2232,2233,2234, |2241,2242,2243,2244, |2311,2312,2313,2314, |2321,2322,2323,2324, |2331,2332,2333,2334, |2341,2342,2343,2344, |2411,2412,2413,2414, |2421,2422,2423,2424, |2431,2432,2433,2434, |2441,2442,2443,2444, |3111,3112,3113,3114, |3121,3122,3123,3124, |3131,3132,3133,3134, |3141,3142,3143,3144, |3211,3212,3213,3214, |3221,3222,3223,3224, |3231,3232,3233,3234, |3241,3242,3243,3244, |3311,3312,3313,3314, |3321,3322,3323,3324, |3331,3332,3333,3334, |3341,3342,3343,3344, |3411,3412,3413,3414, |3421,3422,3423,3424, |3431,3432,3433,3434, |3441,3442,3443,3444, |4111,4112,4113,4114, |4121,4122,4123,4124, |4131,4132,4133,4134, |4141,4142,4143,4144, |4211,4212,4213,4214, |4221,4222,4223,4224, |4231,4232,4233,4234, |4241,4242,4243,4244, |4311,4312,4313,4314, |4321,4322,4323,4324, |4331,4332,4333,4334, |4341,4342,4343,4344, |4411,4412,4413,4414, |4421,4422,4423,4424, |4431,4432,4433,4434, |4441,4442,4443,4444,。
这是个数学上的排列问题。P4=4!=24 用1,2,3,4四个数字可以组成数字不重复和自然数的个数是24个。
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