Question -
Answer -
Given:
Total persons = 10
Number of persons tobe selected = 5 from 10 persons (P1, P2, P3 …P10)
It is also told that P1 shouldbe present and P4 and P5 should not be present.
We have to choose 4persons from remaining 7 persons as P1 is selected and P4 andP5 are already removed.
Number of ways =Selecting 4 persons from remaining 7 persons
= 7C4
By using the formula,
nCr = n!/r!(n – r)!
7C4 = 7! / 4!(7 – 4)!
= 7! / (4! 3!)
= [7×6×5×4!] / (4! 3!)
= [7×6×5] / (3×2×1)
= 7×5
= 35
Now we need to arrangethe chosen 5 people. Since 1 person differs from other.
35 × 5! = 35 ×(5×4×3×2×1)
= 4200
∴ The total no. ofpossible arrangement can be done is 4200.