UPSC Government Jobs Exams undefined

7 candidates are to take examination, 2 in mathematics and remaining in different subjects. In how many ways can they be seated in a row so that the two examinees in Mathematics may not sit together?

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UPSC Other Question
In how many ways can 6 plastic beads of different colours be arranged so that the blue and green beads are never placed together? In how many ways can the letters of the word ‘STRANGE’ be arranged so that the vowels may appear in the odd places?