Let's solve this step-by-step. **Given:** - Total people, \( N = 500 \) - People who like tea, \( T = 285 \) - People who like coffee, \( C = 195 \) - People who like juice, \( J = 115 \) - People who like tea and coffee, \( T \cap C = 45 \) - People who like tea and juice, \( T \cap J = 70 \) - People who like coffee and juice, \( C \cap J = 50 \) - People who don't like any drinks, \( N_{\text{none}} = 40 \) **a) Number of people who like all three drinks:** Let \( x \) be the number of people who like all three drinks (tea, coffee, and juice). We can use the principle of inclusion-exclusion to find \( x \): \[ N_{\text{total}} = T + C + J - (T \cap C) - (T \cap J) - (C \cap J) + x + N_{\text{none}} \] \[ 500 = 285 + 195 + 115 - 45 - 70 - 50 + x + 40 \] \[ 500 = 425 - 165 + x + 40 \] \[ 500 = 300 + x \] \[ x = 500 - 300 \] \[ x = 200 \] So, 200 people like all three drinks. **b) Number of people who like only one drink:** Let's calculate the number of people who like only tea, only coffee, and only juice. **Only tea:** \[ T_{\text{only}} = T - (T \cap C) - (T \cap J) + x \] \[ T_{\text{only}} = 285 - 45 - 70 + 200 \] \[ T_{\text{only}} = 285 - 115 + 200 \] \[ T_{\text{only}} = 370 \] **Only coffee:** \[ C_{\text{only}} = C - (C \cap T) - (C \cap J) + x \] \[ C_{\text{only}} = 195 - 45 - 50 + 200 \] \[ C_{\text{only}} = 195 - 95 + 200 \] \[ C_{\text{only}} = 300 \] **Only juice:** \[ J_{\text{only}} = J - (J \cap T) - (J \cap C) + x \] \[ J_{\text{only}} = 115 - 70 - 50 + 200 \] \[ J_{\text{only}} = 115 - 120 + 200 \] \[ J_{\text{only}} = 195 \] So, the number of people who like only one drink are: - Only tea: 370 - Only coffee: 300 - Only juice: 195