In a cycle race there are 5 persons participated for 5 positions named as J,K,L,M,N.
So that in how many number of ways can make M always before N?

• m is always before n
  it means not only beside may be like this
  3! is for arranging jkl
  m---- 4 positions for n so 4(3!)
  -m--- 3 positions for n so 3(3!)
  --m-- 2 positions for n so 2(3!)
  ---m- 1 position for n so 1(3!)
  
  so 3!(1+2+3+4)=60 ways
• 10 years agoHelpfull: Yes(43) No(3)
• 4! = 24 ans
• 10 years agoHelpfull: Yes(29) No(32)
• m and n taken as one unit then put this one unit in 5 places = 5C2=10
  now in remaing 3 palces, put j k l as 3!=6
  no of ways= 6*10= 60 ways
• 10 years agoHelpfull: Yes(20) No(5)
• j,k,l,(m,n)=4!=24
• 10 years agoHelpfull: Yes(12) No(10)
• Say M came first. The remaining 4 positions can be filled in 4! = 24 ways.
  
  Now M came in second. N can finish the race in 3rd, 4th or 5th position. So total ways are 3 x 3! = 18.
  
  M came in third. N can finish the race in 2 positions. 2 x 3! = 12.
  
  M came in second. N can finish in only one way. 1 x 3! = 6
  
  Total ways are 24 + 18 + 12 + 6 = 60.
• 7 years agoHelpfull: Yes(12) No(0)
• 
  -M--- =3p1*3p3+
  --M--=3p2*2p2+
  ---M=3p3*1
  24+(3*6)+(6*2)+6==24+18+12+6=60
  
• 10 years agoHelpfull: Yes(7) No(1)
• omg..santy...!!!!
  galat ans diya.
• 10 years agoHelpfull: Yes(5) No(2)
• positions -----
  m---- = 4 ways for n
  -m--- = 3 ways for n
  --m-- = 2 ways for n
  ---m- = 1 way for n
  
  ans 10 ways
• 10 years agoHelpfull: Yes(4) No(8)
• Say M came first. The remaining 4 positions can be filled in 4! = 24 ways.
  
  Now M came in second. N can finish the race in 3rd, 4th or 5th position. So total ways are 3 x 3! = 18.
  
  M came in third. N can finish the race in 2 positions. 2 x 3! = 12.
  
  M came in second. N can finish in only one way. 1 x 3! = 6
  
  Total ways are 24 + 18 + 12 + 6 = 60.
  
  Shortcut:
  Total ways of finishing the race = 5! = 120. Of which, M comes before N in half of the races, N comes before M in half of the races. So 120 / 2 = 60.
• 6 years agoHelpfull: Yes(3) No(0)
• Total number of ways in which 5 persons can finish is 5! = 120 (there are no ties)
  Now, in half of these ways M can finish before N.
  so ans is : 60 ways,,,,,,
• 5 years agoHelpfull: Yes(3) No(0)
• ----N 4 ways for M
  ---N- 3 ways for M
  --N-- 2 ways for M
  -N--- 1 ways for M
  total=10 ways
• 10 years agoHelpfull: Yes(2) No(4)
• If M came first. The remaining 4 positions can be filled in 4! = 24 ways.
  Now M came in second. N can finish the race in 3rd, 4th or 5th position. So total ways are 3 x 3! = 18.
  M came in third. N can finish the race in 2 positions. 2 x 3! = 12.
  M came in second. N can finish in only one way. 1 x 3! = 6
  Total ways are 24 + 18 + 12 + 6 = 60.
• 7 years agoHelpfull: Yes(2) No(0)
• 4!=24 ways
• 10 years agoHelpfull: Yes(1) No(2)
• Here,M have always comes before n.So take it as one unit.
  If we take two letters from the set,we get 3 letters(5-2 = 3)
  these 3 units + above one unit(M before N) = 4
  These 4 units can be arranged in 4! ways
  4! = 24 ways.
  Therefore,we can arrange them in 24 ways
• 5 years agoHelpfull: Yes(1) No(0)
• 6!= 720 ans
  
• 10 years agoHelpfull: Yes(0) No(3)
• 4+3+2+1 = 10
• 10 years agoHelpfull: Yes(0) No(3)
• 78 ways:
  ----N =4!=24
  ---N-=3!*3!=36
  --N-- =2!*3!=12
  MN--- =3!=6
  ---
• 10 years agoHelpfull: Yes(0) No(3)
• J K L M N
  
  1 Condition is M > N,
  
  thus N always loose the game by last.
  
  so answer is 4* 5c4 = 20
• 10 years agoHelpfull: Yes(0) No(3)
• Ans: 60
  Sol: Total number of ways in which 5 persons can finish is 5! = 120 (there are no ties)
  Now in half of these ways M can finish before N.
• 6 years agoHelpfull: Yes(0) No(3)