Question

find the
number
of permutations of the
digits 1 to 9 in which nine of the blocks 12,34 and 567 appears
​

Answer 1

Answer:

The total number of permutations of digits 1 through 9 is 9!

The block 34 can occur in 8! ways if we treat "34" as a single symbol in an 8 digit alphabet. Similarly, the block 45 can occur 8! ways and the block 738 can occur 7! ways.

*The blocks 34 and 45 can both occur together if the block 345 is in the permutation. This can occur 7! times.

The blocks 34 and 738 cannot both occur together since 3 can only be used once.

The blocks 45 and 738 can occur together 6! ways by treating 34 and 738 as single symbols in a 6 digit alphabet.

The blocks 34, 45, and 738 cannot all occur together.

Therefore, by Inclusion-Exclusion, the total number of permutations satisfying the conditions is given by:

9!−(8!+8!+7!)+(7!+0+6!)−(0)=282,960

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Answer 2

Answer:

282960

Step-by-step explanation: