In how many ways can 4 men and 3 women can arrange with a condition that each men should not sit together and they must be in the order of their age.

a) 210 b) 5040 c) 120 d) none of these

• d)none of these
  4 men can take 4 position which can be done in 4!
  and women can be sit in 3! ways so 4!*3!
• 9 years agoHelpfull: Yes(32) No(20)
• Given that the total number of people = 7
  First we select 4 positions for the men to occupy.
  These positions could be chosen in 7C4 ways = 7!/4!(7-4)! = (1 x 2 x ... x 7)/(1 x 2 x 3 x 4)(1 x 2 x 3)
  = (5 x 6 x 7)/(1 x 2 x 3) = 35 ways.
  
  This leaves 3 positions for the women, and the women can be rearranged amongst themselves in 3! ways = 6 ways.
  The men, of course, can be in only one order amongst themselves, so the overall number of ways they could line up is given by 35 x 6 = 210 ways.
  Hence, the answer is 210
• 9 years agoHelpfull: Yes(27) No(50)
• answer should be 6 (3!)
  as men arrangement can be made in 1 way only..only the position of women will change
• 9 years agoHelpfull: Yes(27) No(4)
• d) none of these
  no men should come together,this means that there must be a women between each men
  Suppose 'a' is man and 'b' is woman then only possible way is a b a b a b a
  This is the only possible combination
  Therefore women can be arranged in 3! ways and also men can be arranged in 2! ways because their arrangement order may be increasing or decreasing which is not specified in the question .So we have to consider both.
  So answer will be 3! x 2! = 12 ways
  
• 9 years agoHelpfull: Yes(20) No(1)
• 4 men can occupy 7 seats in 7c4 ways but they have to be according to age and men should sit alternatively (MFMFMFM)...so this can be done in 2 ways only...
  3 women can occupy 3 seats in 3c3 ways i.e 3...
  
  so answer is 3*2=6...So D)None Of these...
• 9 years agoHelpfull: Yes(15) No(3)
• ans will be 12 bcoz men are arranging by only 2 method and women are interchanginging by 6
• 9 years agoHelpfull: Yes(6) No(0)
• d)none of these
  4 men-4*3 *2*1
  3 women-3!
  
  
• 9 years agoHelpfull: Yes(3) No(1)
• 4!*3!=144
  so d) is the right option
• 9 years agoHelpfull: Yes(3) No(6)
• Given that the total number of people = 7
  First we select 4 positions for the men to occupy.
  These positions could be chosen in 7C4 ways = 7!/4!(7-4)! = (1 x 2 x ... x 7)/(1 x 2 x 3 x 4)(1 x 2 x 3)
  = (5 x 6 x 7)/(1 x 2 x 3) = 35 ways.
  
  This leaves 3 positions for the women, and the women can be rearranged amongst themselves in 3! ways = 6 ways.
  The men, of course, can be in only one order amongst themselves, so the overall number of ways they could line up is given by 35 x 6 = 210 ways.
  Hence, the answer is 210
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• 9 years agoHelpfull: Yes(3) No(1)
• d) none of these
  as age nt mentioned and it's must A/Q
• 9 years agoHelpfull: Yes(2) No(5)
• First 7 men can be arranged in 7c4 ways= 35 ways. .. Now 3 women can sit in 3!=6 ways.. So total 35*6=210..(a)
• 9 years agoHelpfull: Yes(2) No(1)
• Answer is 3!*2 = 12
  Given condition is that the men are arranged in the order of their age so increasing or decreasing only possible cases i,e. 2 cases and, women arranged in 3! ways.
• 6 years agoHelpfull: Yes(2) No(0)
• a)210
  7C4=35
  7C4*3!=210
• 9 years agoHelpfull: Yes(1) No(14)
• 7C4 * 3! = 210
• 9 years agoHelpfull: Yes(1) No(3)
• answer should be 144 as 24!*6!
• 9 years agoHelpfull: Yes(1) No(3)
• if we fix postion of three girl there will be 4 gap so that 4 gap will be taken but it s given that they will seat in the order of ther age and no men should sit together so no. of ways of arranging women is 3! but for available 4 gap -w-w-w- is occupied by the men according to their age so...if there are 4 man according to there age are (A>B>C>D) so a have only two ways to sit i.e either from last in decresing order,or from first in increasing order so there are so there are 2 ways for ever men so 4*2!=8
  so total number of ways is 8*3!=16 so non of these wii be the answer
• 8 years agoHelpfull: Yes(1) No(0)
• Dear Admin,
  Here it is said that no men can sit together so 7C4 wouldn't work here.
  the answer would be : first 3 women will occupy the seat (3!) then there would be 4 vacant seat for
  a men they can arrange themselves in 4! ways
  so anwer would be 4! 3! = 144 (none of these)
• 6 years agoHelpfull: Yes(1) No(1)
• None of these becz of there is no mention any name
• 9 years agoHelpfull: Yes(0) No(6)
• C) 4!*3!= 120
• 9 years agoHelpfull: Yes(0) No(13)
• the answer is d) none of these because
  for 4 men each should not sit together have four places so 4! = 24
  and in between of two men a woman have to be seated so 3! =6
  so the num of ways is 4!*3!=24*6
  =146
• 9 years agoHelpfull: Yes(0) No(1)
• none of these
  
• 9 years agoHelpfull: Yes(0) No(2)
• Condition of ages is not mentioned in solution
  
• 8 years agoHelpfull: Yes(0) No(1)
• 210
  as bbhjvjhvn
• 6 years agoHelpfull: Yes(0) No(0)
• d)none of these 4 men can take 4 position which can be done in 4! and women can be sit in 3! ways so 4!*3! or Given that the total number of people = 7 First we select 4 positions for the men to occupy. These positions could be chosen in 7C4 ways = 7!/4!(7-4)! = (1 x 2 x … x 7)/(1 x 2 x 3 x 4)(1 x 2 x 3) = (5 x 6 x 7)/(1 x 2 x 3) = 35 ways. This leaves 3 positions for the women, and the women can be rearranged amongst themselves in 3! ways = 6 ways. The men, of course, can be in only one order amongst themselves, so the overall number of ways they could line up is given by 35 x 6 = 210 ways. Hence, the answer is 210
• 6 years agoHelpfull: Yes(0) No(1)
• Since there are no restrictions on how the women are seated, we can arrange the 3 women in 3! ways.
  
  To ensure that no two men are seated together, we need to place the men in the gaps between the women. If we arrange the 3 women, there are 4 possible positions to place the men: one before the first woman, one between each pair of women, and one after the last woman.
  
  We have 4 men to place in these 4 positions, and since they must be in the order of their age, there is only 1 way to arrange them.
  
  Total arrangements=3!×1=6 ways
• 3 Months agoHelpfull: Yes(0) No(0)