A dice is thrown five times.Find the probability of getting only $1.$
Out of five throws,$1XXXX,X1XXX,XX1XX,XXX1X,XXXX1,$where $X$ denotes numbers other than $1.$So the probability of getting only $1$ is $5\times(\frac{1}{6})(\frac{5}{6})^4$
But the answer given in my book is $5\times (\frac{1}{6})^5$,I dont know where i am wrong.
You have correctly calculated the probability of getting exactly one $1$. Note there are two "one"s in the sentence, which is different from the question you asked. I would read "getting only $1$" as rolling $1,1,1,1,1$, which has a probability of $(\frac 16)^5$. I can't think of any way to read the question to get $5(\frac 16)^5$