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01 Feb 2004, 02:45
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source: rutgers.edu
How many permutations are there of the letters in the multiset {M, A, T, H, I, S, G, O, O, D} that dont have words MATH, IS, or GOOD appear as consecutive letters.
How many permutations are there of the letters in the multiset {M, A, T, H, I, S, G, O, O, D} that dont have words MATH, IS, or GOOD appear as consecutive letters.
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01 Feb 2004, 05:38
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total number of perm-10!/2
when only MATH appears-7!/2, only IS-9!/2, only GOOD-7!. When MATH and GOOD appear-4!, MATH and IS-6!/2, GOOD and IS-6!: When all 3 of them appear we have MATH; IS;GOOD-3!. Then the desired figure should be 10!/2-/(7!/2+9!/2+7!)-4!-6!/2-6!-3!x2/. Venn diagram would be useful here.
when only MATH appears-7!/2, only IS-9!/2, only GOOD-7!. When MATH and GOOD appear-4!, MATH and IS-6!/2, GOOD and IS-6!: When all 3 of them appear we have MATH; IS;GOOD-3!. Then the desired figure should be 10!/2-/(7!/2+9!/2+7!)-4!-6!/2-6!-3!x2/. Venn diagram would be useful here.
02 Feb 2004, 12:52
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Quote:
when only MATH appears-7!/2, only IS-9!/2, only GOOD-7!. When MATH and GOOD appear-4!, MATH and IS-6!/2, GOOD and IS-6!: When all 3 of them appear we have MATH; IS;GOOD-3!. Then the desired figure should be 10!/2-/(7!/2+9!/2+7!)-4!-6!/2-6!-3!x2/. Venn diagram would be useful here.
We subtracted too much.
I think it should be -
10!/2-{(7!/2+9!/2+7!)-4!-6!/2-6!+3!x2}
I used the the following ( Venn Diag. Approach)
(A or B or C )= ( A + B+ C ) - {(A and B )+(B and C)+(A and C)} + ( A and B and C)
