Given:
Total persons = 10
Number of persons to be selected = 5 from 10 persons (P1, P2, P3 … P10)
It is also told that P1 should be present and P4 and P5 should not be present.
We have to choose 4 persons from remaining 7 persons as P1 is selected and P4 and P5 are already removed.
Number of ways = Selecting 4 persons from remaining 7 persons
= 7C4
By using the formula,
nCr =\( \dfrac{ n!}{r!(n – r)!}\)
7C4 =\(\dfrac{ 7! }{ 4!(7 – 4)!}\)
= \(\dfrac{ 7! }{ (4! 3!)}\)
= 7×5
= 35
Now we need to arrange the chosen 5 people. Since 1 person differs from other.
35 × 5! = 35 × (5×4×3×2×1)
= 4200
The total no. of possible arrangement can be done is 4200.
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