1. 14 points My Notes Ask Your Toacher An NFL coach sometimes uses a defense tha

Question

1. 14 points My Notes Ask Your Toacher An NFL coach sometimes uses a defense that utilizes S defensive linemen, 3 linebackers, and 3 defensive backs. His roster (the players he can choose from) includes 6 defensive linemen, 5 linebackers, and 8 defensive backs. How many different ways can the coach pick the 11 players to implement this particular defense? 2. -/4 points My Notes Ask Your Mrs. Smith's music class has 10 students. (a) Mrs. Smith wants three of the students in the class to form a trio and play a song for the rest of the class. If any of the students can be selected, how many different trios are possible? (b) Later, Mrs. Smith needs four of the students in the class to form a quartet to work on an upcoming performance. If any of the students can be selected, how many different quartets are possible? 3. -9 points My Notes Ask Your 0 Ann is shopping and has found 6 coats and 7 hats that she likes. (a) If Ann decides to buy one coat and one hat, how many different options does she have for which items she will buy? (b) If Ann decides to buy 2 coats, how many different options does she have for which coats she will buy? (c) If Ann decides to buy 2 of the 6 coats and 2 of the 7 hats, how many different options does she have? (d) If Ann decides to buy 3 items altogether, how many options does she have?

Explanation / Answer

1.

Given

total number of players=19 (6 defensive lineman + 5 line backers +8 defensive backs)

we have to select 11 players (5 defensive lineman+3 line backers +3 defensive bakcs)

For this combination

we can select 5 defensive lineman from 6 in  6C5 ways

we can select 3 linebackers from 5 in 5C3 ways

we can select 3 defensive backs from 8 in  8C3 ways

so total number of ways =6C5 *5C3 * 8C3=6*10*56=3360

2.mrs smith calss has 10 students

a)

we have to select 3 students and each student have equal chance so

it will happen in 10C3 =10*3*4 =120 ways

b)

we have to select 4 students and each student have equal chance so

it will happen in 10C4 =10*3*7 =210 way

3.

HEre total 6 coats and 7 hats liked by ann

a)

If ann decides to by 1 coat and 1 hats so

ann can select 1 coat out of 6 and 1 hat out of 7 in  6C1*7C1=42

b)

if ann decides to by 2 coat

ann select 2 coat out of 6 and zero hat out of 7 in 6C2*7C0=15

c)

If ann decides to by 2 coat and 2 hats so

ann can select 2 coat out of 6 and 2 hat out of 7 in  6C2*7C2=15*21=315

d)

if ann decides to buy 3 items

so ann can select 3 coats or 2 coats and 1 hat or 1 coat and 2 hat ,3 hat

6C3+6C27C1+6C17C2+7C3=20 +15*7 +6*21+35 =20+105 +126 +35 =286

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