## whatisthequestion Group Title Use Pascal's triangle to find the number of ways to choose 5 pens from 7 pens 3 years ago 3 years ago

1. satellite73 Group Title

do you have to write pascals triangle down to level 7? if not just compute $\dbinom{7}{5}=\frac{7\times 6}{2}=21$

2. whatisthequestion Group Title

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

3. satellite73 Group Title

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

4. whatisthequestion Group Title

How am i suppose to know that 21 is the answear doing it that way?

5. satellite73 Group Title

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.

6. whatisthequestion Group Title

okay thank you that makes sense now

7. satellite73 Group Title

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.

8. whatisthequestion Group Title

so the row with just the one is row zero?

9. 3pwood Group Title

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.

10. satellite73 Group Title

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 ...