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From a cloth store, 15 customers bought orange dress, 15 bought red dress, 20 bought blue dress, 2 bought all the three  colours and 8 bought at
Question

From a cloth store, 15 customers bought orange dress, 15 bought red dress, 20 bought blue dress, 2 bought all the three  colours and 8 bought at least two of these. How many bought at least one dress from the store?

A.

45

B.

25

C.

39

D.

40

Correct option is D

Given:
15 customers bought orange dress, 15 bought red dress, 20 bought blue dress, 2 bought all the three colours and 8 bought at least two of these colours.  
Solution:
The shaded portion represent customer who bought atleast two dresses.
=> Customers who bought exactly 2 dresses
= 8 - (2 × 2) = 8 - 4 = 4
Thus we have,
n (O) = 15, n (R) = 15, n (B) = 20
n (O ∩ R ∩ B) = 2
n (O ∩ R) = n (R ∩ B) = n (B ∩ O) = 4
∴ n (O ∪ R ∪ B) = n (O) + n (R) + n (B) - n (O ∩ R) - n (R ∩ B) - n (B ∩ O) + n(O ∩ R ∩ B)
= 15 + 15 + 20 - 4 - 4 - 4 + 2
= 50 - 10 = 40 
Alternate Solution:
Total customers who bought more than at least two colors
=> 8 + 2 = 10
Customers bought clothes of at least one color from the store
=> (15 + 15 +20) - 10
=> 50 - 10 = 40
∴ 40 Customers bought clothes of at least one color from the store.

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