A researcher conducted a survey to 50 respondents about what they like among the three online games, namely the mobile legends, the clash of clans, and the player's unknown battlegrounds (PUBG) out of 50 respondents, 15 people chose PUBG, 30 chose mobile legends and 20 chose clash of clans, How many Respondents chose all 3 online games?

15 Respondents

Step-by-step explanation:

Total number of respondents = n (PUBG ∪ M ∪ C) = 50

PUBG = n(PUBG ) = 15 people

Mobile legends = n(M) = 30 people

Clash of clans = n(C) = 20 people

n ( PUBG ∩ M) = Unknown

Step 1

The first step is to find the number of respondents that chose two or the games

a) Number of respondents that chose Mobile legends and PUBG =

n ( M ∩ PUBG)

30 - x = 15 - x + x

30 - 15 = x + x - x

15 = x

b) a) Number of respondents that chose Mobile legends and Clash of clans =

n ( M ∩ C)

n ( M ∩ C) = y

30 - y = 20 - y + y

30 - 20 = y + y - y

10 = y

c) Number of respondents that chose PUBG and Clash of clans =

n ( C ∩ PUBG) = z

20 - z = 15 - z + z

20 - 15 = z + z - z

5 = z

Step 2

How many Respondents chose all 3 online games

= n ( PUBG ∩ M)

n (PUBG ∪ M ∪ C) = n(PUB ) + n ( M ) + n (C) – n ( M ∩ PUBG) – n ( C ∩ PUBG) – n ( M ∩ C) + n (PUBG ∩ M ∩ C)

50 = 30 + 20 + 15 - 15 - 5 - 10 + n (PUBG ∩ M ∩ C)

50 = 65 - 30 + n (PUBG ∩ M ∩ C)

50 = 35 + n (PUBG ∩ M ∩ C)

50 - 35 = n (PUBG ∩ M ∩ C)

n (PUBG ∩ M ∩ C) = 15

Therefore, the number of Respondents chose all 3 online games = 15

1716

n = 13

r = 6

x(n,r) = c(13,6)

= 13/(6(13-6) = 1716