Question

in a cycle race there are 5 persons named as j, k, l, m, n participated for 5 positions so that in how many number of ways can m make always before n?

Answer 1

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Answer 2

Answer:

60

Step-by-step explanation:

In a cycle race there are 5 persons named as j, k, l, m, n participated for 5 positions so that in how many number of ways can m make always before n?

there are 5 persons

so total number of ways = 5!

= 5 * 4 * 3 * 2 * 1

= 120

out of 120 ways

Either m will be before n or after n

=> m before n = (1/2) * 120 = 60

in total 60 ways m can always make before n

other way to to solve

if m 1st then all can be at any place including n

= 4 * 3 * 2 * 1= 24

if m = 2 then n can be 3 , 4 or 5 & other 3 can be any of the remaining 3 position

= 3! * 3 = 18

if m = 3 then n can be 4 or 5 & other 3 can be any of the remaining 3 position

= 3! * 2 = 12

if m = 4 then n can be  5 & other 3 can be any of the remaining 3 position

= 3! * 1 = 6

m = 5th not possible

So total ways = 24 + 18 + 12 + 6 = 60