Answer:
Step-by-step explanation:
Ben is present in all pictures so rest of 4 persons to be selected from 8 persons , no of ways to do it is
⁸C₄ = 8 x 7 x 6 x 5 / 4 x 3 x 2 x 1
= 70 .
In one of these combination , we can get 5 ! ( five factorial )
Total no of permutations
= 70 x 5 !
= 8400 .
b ) Both Ed and Gail are present
The above derivation changes to the following .
Total no of permutations
= ⁷C₃ x 5 !
= 35 x 120
= 4200
c )
exclude 2 person from 9 to be selected
permutation
= ⁷C₅ x 5 !
= 21 x 120
= 2520
d )
rest of 3 person from 7 persons , no of permutations
⁷P₃ = 7 x 6 x 5 = 210
e )
Hal or Ida can occupy any of the 5 position which can be done in 5 ways .
when one position is occupied , the rest of 4 position can be occupied by 7 persons which can be done in
⁷P₄ ways
Total ways = 5 x ⁷P₄
= 5 x 840
= 4200
f )
They can occupy position like 1,2 or 2,3 or 3,4 or 4,5
Rest of the position can be occupied in ⁷P₃ ways
Total ways = 4 x ⁷P₃
= 4 x 210
= 840
They can also be exchanged mutually so no of ways
= 840 x 2 = 1680 .
g ) No of pictures in which Ann and Ben are present
two position to be selected out of 5 = ⁵P₂
Rest of position that can be shuffled = ⁷P₃
Total no of pictures in which both are present
= ⁵P₂ x ⁷P₃
= 20 x 210
= 4200
out of which they will be standing next to each other = 1680
no of pictures in which they will not be standing next to each other
= 4200 - 1680 = 2520. .
