The girls Amy, Ann, and Doris and the boys Al, Abe, Bob, andRoy are in a nursery

Question

The girls Amy, Ann, and Doris and the boys Al, Abe, Bob, andRoy are in a nursery group. In how many ways can the children bearranged in a line so that a girl is ALWAYS at the head of theline? -i think that the answer might be 3x2x1x4x3x2x1 which equals144...i'm not suree though...pleaseeee help asappp!!! The girls Amy, Ann, and Doris and the boys Al, Abe, Bob, andRoy are in a nursery group. In how many ways can the children bearranged in a line so that a girl is ALWAYS at the head of theline? -i think that the answer might be 3x2x1x4x3x2x1 which equals144...i'm not suree though...pleaseeee help asappp!!!

Explanation / Answer

3 girls and 4 boys The number of possibilities to get a girl at the first site is 3 * 6*5*4*3*2*1 = 2160 Why? First position has to be a girl, so Amy, Ann or Doris, so 3possibilities for position 1. The second position does not care, so there are 6 possibilities.All the boys (4) and two of the remaining girls. This is true for all the other positions, so there are 5 personsfor the third position, 4 for the fourth position etc. Your answer is to the number of possibilities to have first 3 girlsand then 4 boys, because: Again, the first position has to be a girl, so Amy, Ann or Doris,so 3 possibilities for position 1. Then, the second position has to be a girl again, so there are 2possibilities and only 1 for the third position, because the othertwo girls are on position 1 and 2. T hen, there are 4 possibilities for position 4, because it has tobe a boy etc. You can multiply all these possibilties, which gives you3x2x1x4x3x2x1 = 240 for the number of possibilities to have first 3girls and then 4 boys.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.