How many 6-digits positive integers which are formed by the digits 1 to 9 are such that each of the digits in the number appears at least twice? [For instance: 121233,122221,777777 and etc.]


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Question Number 116184 by ZiYangLee last updated on 01/Oct/20

$How many 6 - digits positive integers which are$ $formed by the digits 1 to 9 are such that each$ $of the digits in the number appears at least$ $twice ? [For instance : 121233, 122221, 777777 and etc .]$
	Answered by mr W last updated on 01/Oct/20

	$w e h a v e f o l l o w i n g c a s e s :$ $A A B B C C$ $\Rightarrow C_{3}^{9} \times \frac{6!}{2! 2! 2!} = 7560$ $A A A B B B$ $\Rightarrow C_{2}^{9} \times \frac{6!}{3! 3!} = 720$ $A A A A B B$ $\Rightarrow C_{2}^{9} \times \frac{6!}{4! 2!} = 540$ $A A A A A A$ $\Rightarrow C_{1}^{9} = 9$ $t o t a l l y 7560 + 720 + 540 + 9 = 8829$
	Commented by ZiYangLee last updated on 02/Oct/20

	$★$
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