A closet has 5 pairs of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is

Number of selection with no complete pair = total number of ways of choosing 4 shoes – number of ways in which there is atlest one complete pair. = 10C4−[ 5C1× 8C2− 5C2]     =210−[140−10]=80.