A closet has 5 pairs of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is

Question

A closet has 5 pairs of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is (A) 80 (B) 160 (C) 200 (D) None of these

Tardigrade Admin · Accepted Answer

Select 4 pairs in 5 C4=5 ways. Now select exactly one shoe from each of the pair selected in ( 2 C1)4 ways. This will fulfill the condition. ⇒ required answer =5 × 16=80

Q. A closet has $5$ pairs of shoes. The number of ways in which $4$ shoes can be chosen from it so that there will be no complete pair is

80

160

200

None of these

Select $4$ pairs in $^{5} C_{4} = 5$ ways.
Now select exactly one shoe from each of the pair selected in $(^{2} C_{1})^{4}$ ways.
This will fulfill the condition.
$\Rightarrow$ required answer $= 5 \times 16 = 80$

Q. A closet has 5 pairs of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is

80

160

200

None of these

Select 4 pairs in 5C4​=5 ways. Now select exactly one shoe from each of the pair selected in (2C1​)4 ways. This will fulfill the condition. ⇒ required answer =5×16=80

Q. A closet has $5$ pairs of shoes. The number of ways in which $4$ shoes can be chosen from it so that there will be no complete pair is

Select $4$ pairs in $^{5} C_{4} = 5$ ways.
Now select exactly one shoe from each of the pair selected in $(^{2} C_{1})^{4}$ ways.
This will fulfill the condition.
$\Rightarrow$ required answer $= 5 \times 16 = 80$