a+n+p=12
a,n,p are integers from 1 to 7.Find no. of possible solutions?

• Total no. of solutions - 37
  combinations such as -
  (1,4,7)(1,5,6)(1,6,5)(1,7,4) - 4
  (2,3,7)(2,4,6)(2,5,5)(2,6,4)(2,7,3) - 5
  (3,2,7)(3,3,6)(3,4,5)(3,5,4)(3,6,3)(3,7,2) - 6
  (4,1,7)(4,2,6)(4,3,5)(4,4,4)(4,5,3)(4,6,2)(4,7,1) - 7
  (5,1,6)(5,2,5)(5,3,4)(5,4,3)(5,5,2)(5,6,1)- 6
  (6,1,5)(6,2,4)(6,3,3)(6,4,2)(6,5,1) - 5
  (7,1,4)(7,2,3)(7,3,2)(7,4,1) - 4
  Hence total no.of possible solutions - 37
• 11 years agoHelpfull: Yes(22) No(5)
• possible combinations and their different arrangements are:
  (1,4,7)=3!
  (1,5,6)=3!
  (2,3,7)=3!
  (2,4,6)=3!
  (2,5,5)=3
  (3,4,5)=3!
  (3,6,3)=3
  (4,4,4)=1
  no. of possible solutions= 3!+3!+3!+3!+3+3!+3+1
  = 6+6+6+6+3+6+3+1
  = 37
• 10 years agoHelpfull: Yes(15) No(0)
• Fix a at 1:
  possible set of (n,p)=(1,10),(2,9)....(10,1) =10
  at a=2
  possible set of (n,p)=(1,9),(2,8)....(9,1) =9
  .
  .
  .
  at a=7
  possible set of (n,p)=(1,4),(2,3)....(4,1) =4
  So ans=10+9+8+7+6+5+4
  =49(ans)
• 11 years agoHelpfull: Yes(6) No(28)
• answer=55
  
• 11 years agoHelpfull: Yes(3) No(3)
• a,n,p be have values 1,4,7 -> 3ways
  1,5,6 ->3 ways
  2,3,7->3ways
  2,4,6 ->3
  2,5,5 ->3
  3,3,6 ->3
  3,4,5 ->3
  4,4,4 ->1
  so,total of 22 ways
• 11 years agoHelpfull: Yes(3) No(4)
• 18 ways
  1. 1,4,7 - 3! ways
  2. 1,5,6 - 3! ways
  3. 1,6,5 - 3! ways
  hence 3!+3!+3! = 18 ways
• 11 years agoHelpfull: Yes(2) No(11)
• If repeatition is allowed then 37 and if not then 30
  
• 10 years agoHelpfull: Yes(2) No(0)
• repetition of no. is allowed?
  
• 11 years agoHelpfull: Yes(1) No(1)
• Gaurav Nagdev's solution is nice but requires more time :p Sorry, dude !!!
• 11 years agoHelpfull: Yes(1) No(1)
• 9 solutions
  2+3+5(3tyms)
  2+4+6(3 tyms)
  3+4+5(3 tyms)
• 11 years agoHelpfull: Yes(0) No(12)
• 30 solutions.....
  
• 11 years agoHelpfull: Yes(0) No(3)
• 5 solutions
  7+4+1
  7+3+2
  6+5+1
  6+4+2
  5+4+3
  
• 11 years agoHelpfull: Yes(0) No(3)
• 0,4,8-3! ways
  0,5,7-3!
  1,4,7
  2,3,7
  2,4,6
  3,2,7
  3,4,5
  6,5,1
  6,4,2
  so 9*6= 54 ways..
• 11 years agoHelpfull: Yes(0) No(2)
• 38 is
  ans
  
• 11 years agoHelpfull: Yes(0) No(0)
• (1+4+7),(1+5+6),(1+6+5),(1+7+4)
  (2+3+7),(2+4+6),(2+5+5),(2+6+4),(2+7+3)
  so on...
  total no of solution is 49
• 10 years agoHelpfull: Yes(0) No(0)
• If we consider only positive solution then
  x1+x2+x3+....+xk=n
  then no of solution
  (n-1)
  C
  (k-1)
  if zero is included then non-negative positive solution
  (n+k-1)
  C
  (k-1)
  For this case n=12 and k=3
  then only positive solution
  (12-1)
  C
  (3-1)
  which gives
  55.
• 10 years agoHelpfull: Yes(0) No(0)