In this case out of 16 men and women at least 50% women in the team that means maximum no. of women can be any so we have following cases
Case 1 4 men and 4 women i.e. 8C4x8C4
Case 2 3 men and 5 women i.e. 8C5x8C3
Case 3 2 men and 6 women i.e. 8C6x8C2
Case4 1 men and 7 women i.e. 8C7x8C1
Case5 0 men and 8 women i.e. 8C8
Hence no. of ways team is selected is 8C4x8C4 + 8C5x8C3 + 8C6x8C2 + 8C7x8C1 + 8C8
As only one person catch the train so we have following cases
Case 1 only Ram catch the train i.e. 12∗ 14∗ 35
Case 2 only Ram catch the train i.e. 12∗ 34∗ 35
Case 3 only Ram catch the train i.e. 12∗ 14∗ 25
Hence total probability is (12∗ 14∗ 35)+(12∗ 34∗ 35)+(12∗ 14∗ 25) 340+940+ 240 1440= 720
HCF = common factors lowest power
HCF = 22*11 = 44
Vowels come together = (UIE)JSTC
Ways = 3!*5! = 720
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Smallest possible class strength = LCM of 5, 13 and 17
LCM of 5, 13 and 17 = 1105