Question
Question: A party consists of 2 American, 2 Britishmen, 2 chinese and 4 men of other nationalities. The no. of...
A party consists of 2 American, 2 Britishmen, 2 chinese and 4 men of other nationalities. The no. of ways in which they can stand in a row so that no two men of same nationality are together.
A
∠10 - 6∠9 + 12∠8-8∠7
B
∠10 - 6∠9
C
∠10 + 12∠8
D
∠10 - 8∠7
Answer
∠10 - 6∠9 + 12∠8-8∠7
Explanation
Solution
Total no. of ways, S = ∠10.
S1 = No. of ways in which two persons of atleast one nationality are together.
S2 = No. of ways in which two persons of atleast two nationality are together.
S3 = No. of ways in which two persons of atleast three nationality are together.
S1 = 2∠9 x 3 = 6∠9; S2 = 4∠8 x 3 = 12∠8; S3 = 8∠7.
Required no. of ways = S - S1 + S2 - S3 = ∠10 - 6∠9 + 12∠8 - 8∠7.