anonymous
  • anonymous
Use Pascal's triangle to find the number of ways to choose 5 pens from 7 pens
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
do you have to write pascals triangle down to level 7? if not just compute \[\dbinom{7}{5}=\frac{7\times 6}{2}=21\]
anonymous
  • anonymous
I am pretty sure im suppose to use Pascal's triangle written out and not the formula for this question bu i dont know what in Pascal's triangle would give me the soultion
anonymous
  • anonymous
elsewise you have to write out the whole triangle down to 7 levels 1 11 121 1331 14641 15 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 and the 21 is both the third and 6th entry

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anonymous
  • anonymous
How am i suppose to know that 21 is the answear doing it that way?
anonymous
  • anonymous
the 7th row of pascals triangle is 1 7 21 35 35 21 7 1 the first entry is 1, the number of ways you can choose no things out of 7 the second entry is 7, the number of ways you can choose 1 out of 7 21 is the number of ways to choose 2 out of 7 35 number of ways to choose 3 also 4 etc.
anonymous
  • anonymous
okay thank you that makes sense now
anonymous
  • anonymous
notice also that the number of ways to choose 5 out of seven is the same as the number of ways to choose 2. that is obvious because choosing 5 to include is the same as choosing 2 to exclude.
anonymous
  • anonymous
so the row with just the one is row zero?
anonymous
  • anonymous
Yeah, it helps to think of all the 1s as zero terms. Then for picking 5 objects out of 7, you're looking at entry 5 in row 7.
anonymous
  • anonymous
yes the top is the 'zero' level it is what you get if you expand \[(a+b)^0\] the next level gives \[(a+b)^1=a+b\] the next gives \[(a+b)^2=a^2+2ab+b^2\] and so on. so the '7th' level is the one that starts 1 7 ...

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