through a qualified apprenticeship program or qualified multi-employer apprenticeship program for— (i) the 3 preceding taxable years, or (ii) the number of taxable years in which the qualified apprenticeship program or the qualified multi-employer apprenticeship program was in existence, whichever is less. (3) Denial of double benefit No deduction or any other credit shall be allowed under this chapter for any amount taken into account in determining the credit under this section. (4) Election not to claim credit This section shall not apply to a taxpayer for any taxable year if such taxpayer elects to have this section not apply for such taxable year. (5) Limitation The apprenticeship program credit under this section shall not be allowed for more than 3 taxable years with respect to any qualified individual. (b) Qualified individual (1) In general For purposes of this section, the term qualified individual means, with respect to any taxable year, an individual who is an apprentice and— (A) is participating in a qualified apprenticeship program or a qualified multi-employer apprenticeship program with an employer that is subject to the terms of a valid apprenticeship agreement (as defined in the Act of August 16, 1937 (commonly known as the National Apprenticeship Act