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 1

Answer:

Mr. Smith shook 54 hands

Step-by-step explanation:

28 couples are a group of two people,so, 28 *2 equals to 55, subract his spouse and it will be 54

Answer 2

Number of hands shake Mr. Smith can do is equals to 54 hands as per the data given.

What is permutation ?

"Permutation is the way of arranging the number of given object."

What is combination?

" Combination is the way of selecting the given number of objects."

According to the question,

Total number of couples present in a party = 28

Therefore,

Total number of people = 2 × 28

                                        = 56

Condition given,

Each person can not shake hand with his/her spouse and himself.

Therefore,

Number of hands shake Mr. Smith can do = 56 - 2

                                                                     = 54

Hence, number of hands shake Mr. Smith can do is equals to 54 hands as per the data given.

Learn more about permutation and combination here

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