how many even three-digit integers haver the property that their digits ,read left to right ,are strictly increasing order?

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how many even three-digit integers haver the property that their digits ,read left to right ,are strictly increasing order?
how many even three-digit integers haver the property that their digits ,read left to right ,are strictly increasing order?

how many even three-digit integers haver the property that their digits ,read left to right ,are strictly increasing order?
有多少偶数的三位数整数有如下性质,从左向右读,每个数字递增,距离246
这个直接分类法再加上点排列组合
最後一位只能是24680,要严格递增,所以0不可能,分类如下,首位有1－6,六种可能,（7,8,9都无法构成严格递增的偶数）,中间只能1－7
1（中间不可小於等於1）开头2,3搭配4,6,8；4,5搭配6,8；6,7搭配8
同理继续2开头3搭配4,6,8；4,5搭配6,8；6,7搭配8
3开头4,5搭配6,8；6,7搭配8
4开头5搭配6,8；6,7搭配8
5开头6,7搭配8
6开头7搭配8
最後结果2*3+2*2+2+3+2*2+2+2*2+2+2+2+2+1=34种
我不知道有没有更简单的方法了－－

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