The sophomore lacrosse team has 30 players of whom 12 played

The sophomore lacrosse team has 30 players, of whom 12 played defense last year, 14 played offense, and 4 played both defense and offense, while the rest of the players did not play last year. How many members of the team played last year?

Solution

A dentoe played defense and B denote played offense.

n(A) = No. of played defense = 12,

n(B) = No. of played offense = 14,

n(A and B) = No. of played both defense and offense = 4

Total number of players n(S) = 30.

No. of Played only defense is 12 - 4 = 8 and No. of played only offense = 14 - 4 = 10

The rest players did not play last year is

   n(S) - No. of Played only defense - No. of played only offense - No. of played both defense and offense

= 30 - 8 - 10 - 4 = 8 players who are not played in last year.