Fifteen married couples are at a dance lesson, but now only five men and five women are selected at random, then randomly paired
1 answer:
Answer:
( ¹⁵C₂ )² × 5! = 1082161080
Explanation:
Data provided in the question:
Number of married couples = 15
Therefore,
Number of males = 15
Number of females = 15
Now,
The number of possible dancing arrangements
= Probability of selecting males × Probability of selecting males × ways of arranging 5 pairs
= ¹⁵C₂ × ¹⁵C₂ × 5!
= ( ¹⁵C₂ )² × 5!
= × ( 5 × 4 × 3 × 2 × 1 )
= × ( 5 × 4 × 3 × 2 × 1 )
= × 120
= 1082161080
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Answer: Please refer to Explanation
Explanation:
a) When both Hitachi and Toshiba engage in a limited campaign, they both earn $11 million.
If both engage in an extensive campaign they both earn $8 million.
However, if one firm engages in an extensive campaign and the other firm engages in a limited one, the firm engaging in a limited campaign earns $4 million while the one engaging in an extensive campaign earns $16 million.
I have attached a photo to show the payoff matrix as a table.
b) In the absence of a binding and enforceable agreement, that is to say that if both firms are not colluding, Hitachi's dominant strategy would be to engage in an EXTENSIVE PROMOTIONAL CAMPAIGN.
A Firm's dominant strategy in absence of an agreement is that strategy that a firm can go on and make a maximum amount of profit regardless of what the other firm does.
Should Hitachi engage in an Extensive Campaign, they will make $16 million in quarterly profit if Toshiba engages in a Limited Campaign. Should Toshiba also decide to engage in an Extensive Campaign, then Hitachi makes a profit of $8 million. This is therefore their best alternative as opposed to embarking on a limited Campaign where there is a chance that they will make $4 million.
With the Extensive Campaign, Hitachi's Minimum Payoff is $8 million.
c) The game is the same for both players so the best option for Hitachi, is the best option for Toshiba as well. This means that Toshiba's dominant Strategy is an EXTENSIVE PROMOTIONAL CAMPAIGN and their minimum payoff is $8 million as well.
