To solve this problem, we can use the concept of combinations.
When Emily shakes hands with another child, it can be considered as a handshake between two distinct individuals.
So, the number of handshakes can be calculated by finding the number of combinations of 2 from a group of 10 children.
The formula to calculate the number of combinations is given by:
[ \binom{n}{r} = \frac{n!}{r!(n-r)!} ]
Where n is the total number of individuals (children) and r is the number of individuals (children) in each combination.
In this case, n = 10 and r = 2.
Plugging in the values, we get:
[ \binom{10}{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2!8!} = \frac{10 \times 9}{2 \times 1} = 45 ]
Therefore, the total number of handshakes is 45.
Let's go through each option to understand why it is correct or incorrect:
Option A) 50 - This option is incorrect because the actual number of handshakes is 45, not 50.
Option B) 45 - This option is correct because the actual number of handshakes is 45.
Option C) 100 - This option is incorrect because the actual number of handshakes is 45, not 100.
Option D) 55 - This option is incorrect because the actual number of handshakes is 45, not 55.
The correct answer is B) 45. This option is correct because the actual number of handshakes is 45.