(I) How many TEN-BIT strings of 0\'s and 1\'s are there that begin or end with a

Question

(I) How many TEN-BIT strings of 0's and 1's are there that begin or end with a 1 (or both)? (J) In how many ways can a committee of five persons be selected from eight men and seven women such that at least one man is on the committee? (K) In how many ways can a committee of four persons be chosen from a group of ten men and seven women such that the committee does not have the same number of men on the committee as women (two each)? (L) The University of Tulsa phone numbers look like 631-xxxx where xxxx is the 4-digit extension. How many 4-digit extension numbers are there that have at least one 7 in the extension number? (M) A quiz has 5 questions. How many ways can (integer) points be assigned to the problems if the total points is 20 and each problem is worth at least two points each?

Explanation / Answer

j) this answer is for second Question ..........................hope you understand

we want 5 members in the committee.

now, we want atleast 1 men in the committee i.e.we can 1 or 2 or 3 or 4 or 5 (not more than 5 because committee is only for 5 persons)

now case 1

complete 5 mens in the committe = 8c5

4 men and 1 women = 8c4 * 7c1

3 men and 2 women = 8c3 *7c2

2 men and 3 women =8c2 *7c3

1 men and 4 women = 8c1 * 7c4

there fore total ways = 8c5 + 8c4 * 7c1 + 8c3 *7c2 + 8c2 *7c3 + 8c1 * 7c4

= 56 + (70 *7 ) +(56 * 21) + (28 * 35) + (8 * 35)

=56 + 490+1176 + 980 + 280

=2982 ways

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