There are 66 ways Kim can put the 10 identical lamps on the 3 identical tables
<h3>How to determine the number of ways?</h3>
The given parameters are:
- Identical lamps, n = 10
- Identical tables, r = 3
The combination involving identical objects is calculated using:
(n + r - 1)C(r - 1)
So, we have:
n + r - 1 = 10 + 3 - 1
Evaluate the sum
n + r - 1 = 13 - 1
Evaluate the difference
n + r - 1 = 12
Also, we have:
r - 1 = 3 - 1
Evaluate the difference
r - 1 = 2
So, we have:
(n + r - 1)C(r - 1) = 12C2
Apply the following combination formula:
nCr = n!/((n - r)!r!)
So, we have:
12C2 = 12!/((12 - 2)! * 2!)
Evaluate the difference
12C2 = 12!/(10! * 2!)
Expand the numerator
12C2 = 12 * 11 * 10!/(10! * 2!)
Evaluate the quotient
12C2 = 12 * 11/2!
Expand the denominator
12C2 = 12 * 11/2 * 1
Evaluate the product
12C2 = 132/2
Evaluate the quotient
12C2 = 66
Hence, there are 66 ways Kim can put the 10 identical lamps on the 3 identical tables
Read more about combination at:
brainly.com/question/11732255
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