(1-1/2)*(1-1/3)*(1-1/4)*(1-1/5)*(1-1/6)*(1-1/7)*(1-1/8)*(1-1/9)*(1-1/10),
first solve the brackets,
we will get 1/2*2/3*3/4*4/5*5/6*6/7*7/8*8/9*9/10,
cancel 2 in 1/2 and 2/3,
cancel 3 in 2/3 and 3/4,
cancel 4 in 3/4 and 4/5,
cancel 5 in 4/5 and 5/6,
cancel 6 in 5/6 and 6/7,
cancel 7 in 6/7 and 7/8,
cancel 8 in 7/8 and 8/9,
cancel 9 in 8/9 and 9/10,
now we will get 1/1*1/1*1/1*1/1*1/1*1/1*1/1*1/1*1/1*1/10,
then multiply1*1*1*1*1*1*1*1*1*1/1*1*1*1*1*1*1*1*1*10,
then we will get the answer as 1/10,
so option C is correct.