Question

Question:
There are 28 couples at a party.
Each person shakes hands with every other person,
except their own spouse.
When the party is over, Mr. Smith asks each attendant how
many hands they shook and everyone tells him a different number.
How many hands did Mr. Smith shake?
Answer:
0 27
0
0 1
O 26
0 28
O 53
0 54
O 55​

Answer 1

Given: There are 28 couples at a party. Each person shakes hands with every other person,except their own spouse. When the party is over, Mr. Smith asks each attendant how many hands they shook and everyone tells him a different number.

To find: How many hands did Mr. Smith shake?

Solution: A couple consists of two persons. Since there are 28 couples in the part, therefore, total number of people at this party

= 28 × 2

= 56 people

As mentioned, Mr. Smith shakes hand with everyone in the party except his spouse. Therefore, he shook hands with all the other 27 couples at the party since they were the 28th couple.

Therefore, total handshakes by Mr. Smith

= 27 × 2 people

= 54 people

Therefore, Mr. Smith shakes option (e) 54 hands.

Answer 2

Answer:

The total hand shakes done  by Mr smith is 54.

Given:

There are 28 couples at a party. Each person shakes hands with every other person, except their own spouse.

To Find :

How many hand shakes done by Mr Smith

Step-by-step explanation:

As there are 28 couples in the party , therefore total number of persons in the party is equal to 28 x 2 = 56  persons

When the party is over, Mr. Smith asks each attendant how many hands he shook with the other members of the part at that night.

If we take Mr Smith , then he will shake hand with every one except with himself and his wife , means he will hand shake with rest of the persons.

Rest of the persons are  =  total members - Mr Smith - Mrs Smith's wife

= 56 - 1 -1

= 56 -2

= 54

So total number of hand shakes done by Mr Smith will be equal to the rest of the members.

Hence the total hand shakes done  by Mr smith is 54.