Question

A person always prefers to eat 'parantha' and ’vegetable dish’ in his meal on Monday, Tuesday and Wednesday but on other days he adds salads to his meal.
How many ways can he make his platter in a marriage party if there are three types of paranthas, four types of ‘vegetable dish’, three types of ’salads’ and two types of ‘sauces’ ?

• A. If the marriage party is on Monday, then he can make his platter in $3360$ ways
• B. If the marriage party is on Sunday, then he can make his platter in $3360$ ways
• C. If the marriage party is on Sunday, then he can make his platter in $2940$ ways
• D. If the marriage party is on Monday, then he can make his platter in $3300$ ways

Answer 1

Answer: (A), (C)

If the marriage party is on Sunday, then he can make his platter in $2940$ ways

The number of ways he can select at least one parantha $=2^3-1=7.$

The number of ways he can select at
least one vegetable dish $=2^4-1=15.$

The number of ways he can select zero or more items from sauces $=2^2=4$.

Case $1:$ If the marriage party is either on Monday or Tuesday or Wednesday.
The number of ways he can select zero or more items from salads $=2^3=8$.

Hence, the total number of ways is $7\times 15\times 8\times 4=3360.$

Case $2:$ If the marriage party is other than Monday, Tuesday and Wednesday.
The number of ways he can select one or more items from salads $=2^3-1=7$.

Hence, the total number of ways is $7\times 15\times 7\times 4=2940.$