Overview 1 2 3 $4 \quad 5$ 6 7 8 9 10 11 Question Progress Homework Progress 15 / 39 Marks A survey conducted in a school asked whether pupils played tennis (T) or badminton (B) last week. - 18 played badminton. - 6 did not play tennis or badminton. - 21 played tennis. - 5 played both tennis and badminton. Some of this information is already shown in the Venn diagram. Work out how many pupils were in the survey. Optional working Answel

Step 1 ：Given information:

Step 2 ：\(B = 18\) pupils played badminton

Step 3 ：\(N = 6\) pupils did not play tennis or badminton

Step 4 ：\(T = 21\) pupils played tennis

Step 5 ：\(B \cap T = 5\) pupils played both tennis and badminton

Step 6 ：Find the number of pupils who played only badminton and only tennis:

Step 7 ：\(B - (B \cap T) = 18 - 5 = 13\) pupils played only badminton

Step 8 ：\(T - (B \cap T) = 21 - 5 = 16\) pupils played only tennis

Step 9 ：Find the total number of pupils in the survey:

Step 10 ：\(Total = B + T - (B \cap T) + N = 13 + 16 + 5 + 6 = 40\)

Step 11 ：\(\boxed{40}\) pupils were in the survey