Question

A-One Talent Agency has 108 clients. 42 of the clients play piano and 51 of the clients play guitar.

Answer 1

Thwre are 28 clients who don not play any of the instrument using the principle of Venn distribution.

Using a Venn diagram analogy :

• Total number of client, U = 108
• Piano, P = 42
• Guitar, G = 51
• Piano and Guitar, (PnG) = 13
• None =?

From the information given :

• P only = 42 - 13 = 29
• G only = 51 - 13 = 38

The total number of clients can be related thus :

• Total = P only + G only + PnG + None

108 = 29 + 38 + 13 + None

108 = 80 + None

None = 108 - 80

None = 28

Therefore, the number of clients who do not play any of the instruments is 28

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