When six fairs coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads ?

The question requires you to find number of the outcomes in which at most 3 coins turn up as heads.
i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads.

The number of outcomes in which 0 coins turn heads is  $6C0$=1 

The number of outcomes in which 1 coin turns head is = $6C1$=6 

The number of outcomes in which 2 coins turn heads is $6C2$=15 

The number of outcomes in which 3 coins turn heads is $6C3$=20

Therefore, total number of outcomes =1+6+15+20= 42 outcomes