Number of A’s Number of B’s Number of C’s Number of D’s Number of E’s Number of F’s Number of G’s Number of H’s = = = = = = = = 5 5 4 4 3 1 1 1
Find the number of 5 lettered words which you can make from the above given set of letters .
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You should try my problem "fun with numbers" i am sure u will like it
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I just tried all three of them.Could do two correctly.part 2 was tricky :) nice questions
Nice seems you are quite versed with PIE as i hesitate in using it ! :)
Using the exponential generating function:
G ( x ) = ( 1 + x + 2 ! x 2 + 3 ! x 3 + 4 ! x 4 + 5 ! x 5 ) 2 ( 1 + x + 2 ! x 2 + 3 ! x 3 + 4 ! x 4 ) 2 ( 1 + x + 2 ! x 2 + 3 ! x 3 ) ( 1 + x ) 3
the solution is [ 5 ! x 5 ] G ( x ) = 2 0 3 5 7 7 × 5 ! = 2 1 4 6 2
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This one is interesting :P If you have not done part 1 ,I would recommend you to do that first then you would understand this better. when you see the 1's in F,G and H ; the first thing that should come to your mind is making cases. so case 1:when none of F,G and H is taken total no. of ways=5^5-(4x5+3)=3102[PIE]
case 2:when one of F,G and H are taken total no. of ways=3x5x(5^4-1)=9360
case 3: when two of F,G and H are taken total no. of ways=3x5p2x5^3=7500
case 4:when all three of F,G and H are taken total no. of ways=5c2x3!x5^2=1500
therefore,answer=sum of individual answers=21462