Permutations and Combinations:

1. David has 3 shirts and 2 sweaters. In how many ways he can wear either a shirt or a sweater?

Sol:  Shirts (or )Sweaters

3 ways  + 2 ways = 5ways.

2. David has 3 shirts and 2 sweaters. In how many ways he can wear a shirt and a sweater?

Sol: shirts (and) sweaters

3ways * 2 ways = 6ways.

3. In how many ways 5 different chocolates can be distributed to 4 children such that any child can get any no. of chocolates?

Sol:    children        C1      C2     C3      C4

Chocolates     x1       x2       x3       x4          x5

4ways *4  *   4    *   4    *     4       => 4⁵ = 1024.

4. A new flag with six vertical stripes is to be designed using some or all of the colors yellow, green, blue, and red. The no. of ways this can be done such that no two adjacent stripes have the same colour.

Sol:

      4                3                 3               3                3                   3                                   =>4* 3⁵ =>4 *243

5. In how many ways 5 boys can sit in 5 chairs which are in a row.

Sol:                                  B1          B2           B3           B4           B5

CHAIRS : 5ways *   4ways  * 3ways  * 2ways  * 1 way  =  5!

N objects can be arranged in n places in n!  ways.

5. In how many ways 5 prizes (1^st, 2nd,3^rd, 4^th, 5^th) can be given to 5 girls ( A, B, C, D, E). Such that, each girl gets one prize.If 1^st prize cannot be given to girl A or B.

Sol: