What is the difference between the following two questions and how to solve both of them Q1) Two boys - Maths - Permutations and Combinations

Question

What is the difference between the following two questions and
how to solve both of them
Q1) Two boys and four girlsare to be seated in a row in such a
way that no two boys are together How many seating arrangements are
possible?
Q2) For a soccer match between German and Argentina, 7 Germans
and 5 Argentines are standing at the ticket counter to buy the
tickets Every ticket bears a seat no and the people with tickets
bearing consecutive seat no s sit together The person issuing
tickets at the counter is advised not to issue tickets bearing
consecutive seat no s to two Argentines In how many ways can the
tickets be issued?

Aakash Sharma · Accepted Answer

(1) Four girls can be seated in a row in ${}^{4}{P_{4}} = 4!$ ways In each of these arrangements 5 places are created shown by the X mark X G X G X G X G X Since no two boys are to sit together, So we may arrange 2 boys in 5 places This can be done in ${}^{5}{P_{2}}$ ways i e 2 boys can be seated in ${}^{5}{P_{2}}$ ways Hence, the total number of seating arrangements $= {}^{4}{P_{4}} \times {}^{5}{P_{2}} = 4! \times 5 \times 4 = 480$ (2) 7 Germans can be seated in a row in ${}^{7}{P_{7}} = 7!$ ways In each of these arrangements 8 places are created shown by X mark X G X G X G X G X G X G X G X Since no two Argentines are to sit together, so we may arrange 5 Argentines in 8 places This can be done in ${}^{8}{P_{5}}$ ways i e 5 Argentines can be seated in ${}^{8}{P_{5}}$ ways Hence total number of ways $= {}^{7}{P_{7}} \times {}^{8}{P_{5}}$ = 7! Ã— 8 Ã— 7 Ã— 6 Ã— 5 Ã— 4 = 33868800