When a coin is tossed there are two possibilities.- it is either a head or tail and probability of getting either head or tail is #1/2#.
If a coin is tossed twenty times, if we get #17# tails, it means on remaining #3# occasions, we get heads. Hence, probability of getting #17# tails out of #20# tosses is same as getting #3# heads out of #20# tosses.
The probability of getting #k# heads (or tails as probability for either of them is equal i.e. #1/2#) out of #n# trials (i.e. tosses) is given by
#P(n,k)="^nC_k(1/2)^k(1/2)^(n-k)#, where #"^nC_k=(n!)/(k!(n-k)!)#
Hence probability of getting #17# tails from #20# tosses is
#(20!)/(17!3!)(1/2)^17(1/2)^3#
= #(20xx19xx18)/(1xx2xx3)xx(1/2)^20#
= #(20xx19xx3)/2^20#
= #1140/1048576=285/262144=0.0010872#
