Use Pascal's triangle to find the number of ways to choose 5 pens from 7 pens
Stacey Warren - Expert brainly.com
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do you have to write pascals triangle down to level 7? if not just compute
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
elsewise you have to write out the whole triangle down to 7 levels
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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How am i suppose to know that 21 is the answear doing it that way?
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
okay thank you that makes sense now
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.
so the row with just the one is row zero?
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.
yes the top is the 'zero' level it is what you get if you expand
the next level gives
the next gives
and so on. so the '7th' level is the one that starts
1 7 ...