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A-One Talent Agency has 108 clients. 42 of the clients play piano and 51 of the clients play guitar.
13 clients play both the piano and the guitar. How many of the clients do not play either instrument?

Answer :

FICHOHIN

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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