Question

1/10:Lucy wants to wear different clothes every day. She has 8 dresses, 7 pairs of shoes and 3 pairs of earrings Lucy could choose I dress, 1 pair of shoes and 1 pair of earrings every day. However, 1 dress and 1 pair of shoes don't look pretty together, so they cannot be selected together. In such circumstances, for how many days can she wear outfits differently?​ please answer

Answer 1

Answer:

dresses, 7 pairs of shoes and 3 pairs of earrings Lucy could choose I dress, 1 pair of shoes and 1 pair of earrings every day. However, 1 dress and 1 pair of shoes don't look retty together, so they cannot be selected together

Answer 2

Given a the number of dresses, shoes and earrings, find the number of days to wear different outfits

Explanation:

1. in order to wear different outfits each day Lucy need to make different combinations out of the given dresses, shoes and earrings.
2. since one dress and one pair of shoes does not look good together we should remove the combination involving the pairing of these two.
3. number of dress is given $8$, hence number ways to select a dress out of these is                $^8C_1=\frac{8!}{1!(8-1)!}=8$  
4. similarly, we have $7$ pair of shoes and $3$ pair of earrings.
5. hence, number of ways to select a pair of shoes and earrings are $7\ and\ 3$ respectively.
6. now, the invalid combination are $3$ as dress and shoes' combination is fixed but earrings are still considered.
7. hence, total number of combination 'C' is,                                                            [tex]C=8(7)(3)-3\\ C=165[/tex]  ------>ANSWER