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Prime minister office hosted a media conference; in the press conference every media person shakes hands with every other media persons. If there was a total of 300 handshakes in the conference, find the number of media persons who were present in the conference.

Prime minister office hosted a media conference; in the press conference every media person shakes hands with every other media persons. If there was a total of 300 handshakes in the conference, find the number of media persons who were present in the conference. Correct Answer 25

Given:

Total handshakes in the party = 300

Formula used:

Combination formula nCr = n!/(n – r)! r!

Calculation:

Let the media person present in the conference = n

Every person shakes hand with every other person.

Then, total number of handshakes = nC2 = n (n−1)/2

⇒ 300 = n (n−1)/2

⇒ n (n−1) = 600

⇒ n2- n – 600 = 0

⇒ n2- n – 600 = 0

⇒ (n- 25) (n + 24) = 0

⇒ n = 25 (Since n cannot be negative)

∴ There were 25 media persons in the conference.

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