SOLUTION: i need help with these two problems can someone help me.thanks Problem #1 A group of 7 workers decides to send a delegation of 2 to their supervisor to discuss their greivances

Question 87096: i need help with these two problems can someone help me.thanks
Problem #1
A group of 7 workers decides to send a delegation of 2 to their supervisor to discuss their greivances.
a) how many delegations are possible?
b)If it is decided that a particular worker must be in the delegation, how many different delegations are possible?
c)IF there are 2 women and 5 men in the group, how many delegations would include at least 1 woman?
Problem #2
A television commercial for Little Caesars
pizza announced that with the purchase of two pizzas, one
could receive free any combination of up to five toppings
on each pizza. The commercial shows a young child waiting
in line at Little Caesars who calculates that there are
1,048,576 possibilities for the toppings on the two pizzas.*

a. Verify the child�s calculation. Use the fact that Little
Caesars has 11 toppings to choose from. Assume that the
order of the two pizzas matters; that is, if the first pizza
has combination 1 and the second pizza has combination
2, that is different from combination 2 on the first pizza
and combination 1 on the second.

b. In a letter to The Mathematics Teacher, Joseph F. Heiser
argued that the two combinations described in part a
should be counted as the same, so the child has actually
overcounted. Give the number of possibilities if the
order of the two pizzas doesn�t matter.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Problem #1
A group of 7 workers decides to send a delegation of 2 to their supervisor to discuss their greivances.
a) how many delegations are possible?
Answer: 7C2 = 21
-----------------------
b)If it is decided that a particular worker must be in the delegation, how many different delegations are possible?
Answer: 1*6 = 6
--------------------
c)IF there are 2 women and 5 men in the group, how many delegations would include at least 1 woman?
Answer: # of at least 1 woman pairs = # of pairs - # of 2 man pairs
# of at least 1 woman pairs = 21 - 5C2 = 21-10 = 11
--------------------------
Problem #2
A television commercial for Little Caesars
pizza announced that with the purchase of two pizzas, one
could receive free any combination of up to five toppings
on each pizza. The commercial shows a young child waiting
in line at Little Caesars who calculates that there are
1,048,576 possibilities for the toppings on the two pizzas.*
a. Verify the child�s calculation. Use the fact that Little
Caesars has 11 toppings to choose from. Assume that the
order of the two pizzas matters; that is, if the first pizza
has combination 1 and the second pizza has combination
2, that is different from combination 2 on the first pizza
and combination 1 on the second.
# of combinations on one pizza = 11C1+11C2+11C3+11C4+11C5 = 1023
# of combinations on the two pizza = 1023*1023 = 1,046,529
If order makes a difference you get 2*1046529=2,093,058
b. In a letter to The Mathematics Teacher, Joseph F. Heise
argued that the two combinations described in part a
should be counted as the same, so the child has actually
overcounted. Give the number of possibilities if the
order of the two pizzas doesn�t matter.
Looks like 1,046,529 to me.
==============
Cheers,
Stan H.

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