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A four digit number (with no repetitions) is to be formed from the set of numbers {0,1,2,3,4,5,6,7}. Find the probability that the number

Ais even
Bis odd
Cis less than 4000
Dis less than 4000, given that it is greater than 3000

Verified Answer :

syed514

even # --------- if it ends with 0, # of ways = 654 = 120 if not, 3 ways for ending digit, 5 ways for 1st digit, 54 for middle digits = 300 
so total ways = 420 
odd # --------- 4 ways of ending digit, 5 ways for 1st digit, 54 for middle digits = 400 ways 
< 4000: ---------- 3 ways for starting digit, 654 ways for remaining digits = 360 ways 
> 3000 & < 4000 ------------------------ 1 way for starting digit , 654 for remaining digits = 120 ways 

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