Permutation and CombinationHard

Question

Identify the correct statement(s). 

Options

A.Number of zeroes standing at the end of 125 ! is 30.
B.A telegraph has 10 arms and each arm is capable of 9 distinct positions excluding the position of rest. The number of signals that can be transmitted is 1010 - 1.
C.Number of numbers greater than 4 lacs which can be formed by using only the digits 0, 2, 2, 4, 4 and 5 is 90.
D.In a table tennis tournament, every player plays with every other player. If the number of games played is 5050 then the number of players in the tournament is 100.

Solution

First find no. of ′2′ at the end of (125)! is
(A) +
= 62 + 31 + 15 + 7 + 3 + 1 + 0 = 119
Find the number of ′5′ at the end of (125)! is
+ ........ = 25 + 5 + 1 = 31
Hence no. of zero is 31
(B) Total no. of singals can made by each arm = 10 so total number of different signals can be formed = 1010 - 1
(here - 1 is because if all arms are at the poisition of rest, then no signal will pass away)
(C)        
             = 60                         = 30
Total number of arrangement = 90
(D) Let number of player is n
then total number of games is nc2 = 5050  →  n = 101

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